Workbook in Solving Algebraic Expression

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OBJECTIVES OF BACHELOR OF SECONDARY EDUCATION

Produce graduate who can demonstrate and practice the

professional and ethical requirement for the Bachelor of Secondary Education such as: 1.To serve as positive and powerful role models in the pursuit of the learning thereby maintaining high regards to professional growth.2. Focus on the significance of providing wholesome and desirable learning environment.3.Facilitate learning process in diverse type of learners.4.Used varied learning approaches and activities, instructional materials and learning resources.5.Used assessment data, plan and revise teaching – learning plans.6.Direct and strengthen the links between school and community activities.7.Conduct research and development in Teacher Education and other related activities.

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FOREWORD

This Teacher’s Visual Presentation Hand-out entitled “Workbook in Solving Algebraic Expression for Second Year High School” is part of the requirements in Educational Technology 2 under the revised curriculum for Bachelor in Elementary Education based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational Technology 2 is a three (3)-unit course designed to introduce both traditional and innovative technologies to facilitate and foster meaningful and effective learning where students are expected to demonstrate a sound understanding of the nature, application and production of the various types of educational technologies.

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The students are provided with guidance and assistance of selected faculty members of the College through the selection, production and utilization of appropriate technology tools in developing technology-based teacher support materials. Through the role and functions of computers especially the Internet, the student researchers and the advisers are able to design and develop various types of alternative delivery systems. These kind of activities offer a remarkable learning experience for the education students as future mentors especially in the preparation of instructional materials.

The output of the group’s effort may serve as an educational research of the institution in providing effective and quality education. The lessons and evaluations presented in this module may also function as a supplementary reference for secondary teachers and students.



FOR-IAN V. SANDOVAL Computer Instructor / Adviser

Educational Technology 2

DELIA MERCADO Module Consultant Principal of Laboratory High School

LYDIA R. CHAVEZ Dean College of Education

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ACKNOWLEDGEMENT

The authors wish to acknowledge the following persons who gave them the inspiration and the strength to write this module:

The Education Faculty of Laguna State Polytechnic University whose insights inspired the writers to finished this module;

Prof. Lydia R. Chavez, Dean of College of Education for appreciating and checking our workbook.

Mr. For Ian Sandoval, Module Adviser for assisting us in finishing our workbook.

Mrs. Delia Mercado, Module Consultant for checking and giving pieces of advice in making our workbook.


Dr. Corazon N. San Agustin, an Educational Technology professor for being the first one who teach us to make a module.

Friends who helped to finished this module.

The authors’ families who inspired them and ignited their desire to pursue their passion for writing; and

Lastly, to the Lord God Almighty who is the source of enlightenment and inspiration.

THE AUTHORS


INTRODUCTION

This workbook is composed of activities in understanding and analyzing different terminologies and concepts in algebraic expression, solving algebraic expression using fundamental operations, solving algebraic expression using synthetic methods, and simple types of factoring. The workbook is designed to give the learner an opportunity to develop himself in solving mathematical problems in algebra most especially in algebraic expression. The exercises in understanding and analyzing different terminologies and concepts in algebraic expression, solving algebraic expression using fundamental operations, solving algebraic expression using synthetic methods, and simple types of factoring are for the student’s self improvement. The exercises were designed to give the learner ample exercises to develop skill in solving algebraic expressions and mathematical problems in algebra.


GENERAL OBJECTIVESIn this workbook entitled “Workbook in Solving Algebraic

Expression for Second Year High School Students” the students are expected to:

1. Differentiate concept and terminologies in algebraic expression.

2. Measure proficiency in analyzing the function of terminologies in algebraic expression.

3. Avoid guessing an answer in true or false.

4. Define different terminologies in algebraic expression.

5. Analyze the standards in answering fill in the blanks test.

6. Explore the knowledge of the students in analyzing the concepts and terminologies in algebraic expression.


7. Recognize the different terms of a polynomial.

8. Write a monomial, binomial and trinomial equation.

9. Specify if the equation is a monomial, binomial or trinomial.

10. Define different terms of polynomial.

11. Compare monomial to binomial, binomial to trinomial.

12. Improve the abilities in comparing monomial to binomial and binomial to trinomial.

13. Write different equation of a polynomial in a monomial, binomial and trinomial.

14. Identify different terms of polynomials.

15. Increased proficiency in comparing monomial, binomial and trinomial


16. Recall the different degree of polynomial.

17. Have confidence to their self to find the correct answer.

18. Improve the abilities in matching an equation to each degree of polynomials.

19. Identify degree of polynomials.

20. Select the best answer in identifying the degree of polynomial.

21. Have patient in answering multiple choice test.


TABLE OF CONTENTS

Vision, Mission, Goals and ObjectivesForeword

Acknowledgement

Introduction

General Objectives

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Chapter I

Understanding and Analyzing Different Terminologies in Algebraic

ExpressionPre Test IActivity 1Activity 2Activity 3Activity 4Activity 5Activity 6Activity 7


Chapter II

Solving Algebraic Expression Using

Fundamental Operations

Post Test I

Activity 10

Pre Test II

Activity 11

Activity 14

Activity 12Activity 13

Activity 9

Activity 8


Activity 18

Activity 19

Activity 20

Activity 21

Post Test II

Activity 15

Activity 17

Activity 16


Activity 24

Activity 25

Activity 26

Activity 27

Activity 28

Chapter III

Using Synthetic Method in Solving Algebraic Expression

Activity 23

Activity 22

Pre Test III


Activity 32

Activity 33

Activity 34

Activity 35

Activity 36

Post Test III

Activity 31

Activity 30

Activity 29


Chapter IV

Simple Types of Factoring of Algebraic Expression

Pre Test IV

Activity 37

Activity 38

Activity 39

Activity 40

Activity 41

Activity 42

Activity 43


Post Test IV

Activity 44

Activity 45

Activity 46

Activity 47

Activity 48

Activity 49

Activity 50

Activity 51

Activity 52

Activity 53

Activity 54

About the Author

References


Final

Pre Test IName: __________________________Score: _____________Date:

_______________Year and Section: ____________________Teacher:

___________________________

Objectives:

1.To define the different terminologies in algebraic expression;

2.To illustrate different expressions;

3.To analyze different equations and figure out what are the characteristics of an expressions; and

4.To increase proficiency in analyzing the functions of an algebraic expressions.

Objectives:


2.To illustrate different expressions;

3.To analyze different equations and figure out what are the characteristics of an expressions; and


TABLE OF CONTENTSTABLE OF CONTENTS


A , BA , B C , DC , D E , FE , F

G , HG , H II

A. Instruction: Tell whether the statements below are true or false by writing A if the statements is correct and B if the statement is incorrect.

__________1. Variable is any number that is used to represents any element of a given polynomial.

__________2. Exponent is positive or negative integer, written in the upper left of letters or symbols.

__________3. Numerical coefficient is a letter or symbol.

__________4. Literal coefficient is a number.

__________5. Like terms are terms which differ only in their literal coefficient.

PREVIOUSPREVIOUS NEXTNEXT ANWERSANWERS

B. Instruction: Match the given symbols and numbers in column A to its corresponding concepts and terminologies in column B.

A B

____1. a, b, c, x, y, z a. Algebraic Expression

____2. 2, 4, 6, 10, 20 b. Numerical

____3. 5x² + y, 6x²y + 5y c. Exponent

____4. 6x³ + 4y, the number

raise on the upper right of the

variable x is called____________. d. Second term

____5. 5x² - 8x + 2 e. Variables

C. Instruction: Identify the terms and terminologies stated in each number. Write your answer in the space provided before the numbers.

____________1. It is a number in a given polynomials and they are real numbers in a polynomial.

____________2. It is a letter or symbol coefficient containing non-negative power or exponent.____________3. It is a polynomial containing only one term.____________4. It is any letters or symbols that are used to represents any element of a

polynomial.____________5. It is a combination of variables and constants which involved of finite numbers

of indicated operation raise with a power and extract of square root.


D. Instruction: Multiple Choice. Write A if the expressions is monomial B if it is binomial and C if the expressions is trinomial

_____1. 7x² - 9

_____2. 4xy

_____3. 6mn + 1

_____4. 86x² + 43xy + 20y

_____5. 8k³ + 6s² + 4y

F. Instruction: Identify the polynomials in column A to its corresponding terms in column B. Write your answer in the space provided

A B_____ 1. xy a. trinomial_____ 2. 5x² - 8y + 2 b. binomial_____ 3. 7x² + y c. monomial_____ 4. Monomial d. 4ab_____ 5. Trinomial e. 6v³ + 5x – 9


E. Instruction: Identify the terms of polynomials. Write your answer in the space provided before each number.

__________ 1. 6x² - 8

__________ 2. 5x² + 35xy + 25y²

__________ 3. 9xy

__________ 4. 8x² + 10x

__________ 5. 7x² + 5xy + 9y²

G. Instruction: Identify the polynomial in column A to its corresponding degree in column B. Write your answer in the space provided.

A B_____ 1. 7x³y a. 9th degree

________ 2. 21a⁶b³ + 14ab² + 1 b. 7th degree

________ 3. 4x² c. 4th degree

________ 4. 7yz⁵ + 2x³y d. 6st degree

________ 5. 16x⁶y + 4x³y² + 2y e. 2th degree


H. Instruction: Multiple Choice. Identify the degree of the polynomials. Encircle the correct answer.

1. 20x⁶a³ + 10x⁴a³ - a²x

a. 2nd degree b. 7th degree c. 9th degree

2. xyz

a. 1st degree b. 2nd degree c. 3rd degree

3. 8x² - 6x³y² + 4y⁵

a. 3rd degree b. 4th degree c. 5th degree

4. x⁵ - y⁸

a. 6th degree b. 7th degree c. 8th degree

5. 5x² + 4y⁶

a. 1st degree b. 3rd degree c. 6th degree

I. Instruction: Identify the degrees of polynomials. Write your answer in the space provided.

__________ 1. 15x⁵a + 8x⁴a⁴ - a³x__________ 2. 5x⁴y² - 7x⁵y⁴ + 13x²y⁵__________ 3. 12x³y⁸ + 24x⁶y⁴__________ 4. 16x⁴y³z²__________ 5. 5x² + 4y⁶


Answers

QUESTIONSQUESTIONS

QUESTIONSQUESTIONS

QUESTIONSQUESTIONS QUESTIONSQUESTIONS

A.

1.B2.B3.B4.B5.B

B.

1. e2. b3. a4. c5. d

C.

1. constant2.Literal coefficient3. monomial4. variable5. polynomials

D.

1. B2. A3. B4. C5. C

QUESTIONSQUESTIONS

QUESTIONSQUESTIONS

QUESTIONSQUESTIONS

QUESTIONSQUESTIONS

QUESTIONSQUESTIONS

G.

1. c2. a3. e4. d5. b

H.

1. c2.c3.c4.c5.c

F.

1. binomial2. trinomial3. monomial4. binomial5. trinomial

E.

1. c2. a3. b4. d5. e

I.

1. 8th degree2. 9th degree3. 11th degree4. 9th degree5. 6th degree

Activity 1Name: __________________Score:_____________Date: ____________

Year and Section: _______________Teacher:______________________Objectives:

1. To differentiate concept and terminologies in algebraic expression.

2.To measure proficiency in analyzing the function of terminologies in algebraic expression

3. To avoid guessing an answer in true or false test.

Objectives:

1. To differentiate concept and terminologies in algebraic expression.

2.To measure proficiency in analyzing the function of terminologies in algebraic expression

3. To avoid guessing an answer in true or false test.

Instruction: Tell whether if the statements below are true or false. Write A if the statements is correct and B if the statement is incorrect.

_____________1. Variable is any numbers that are used to represents any of element of a given polynomial.

PreviousPrevious NextNextTABLE OF CONTENTSTABLE OF CONTENTS

_____________2. Exponent is positive or negative integer, written in the upper left of letters or symbols._____________3. Numerical coefficient is a letter or symbol._____________4. Like term is a term which differ only in their literal coefficient._____________5. Polynomial is an algebraic expression involves non-negative powers._____________6. Coefficient is the factor of product of a polynomial._____________7. Constant is a number in a given polynomial._____________8. Constant is a real number in a polynomial._____________9. Numerical coefficient is constant coefficient._____________10. Literal coefficient is a number.

AnswersAnswers

QuestionsQuestions

Answers1. B2. B3. B4. B5. A6. A7. A8. B9. A10. A

Activity 2Name:__________________________Score:_____________Date:____________

___Year and Section: ________________ Teacher:

______________________________

Objectives:

1.To recall different terminologies in algebraic expression.

2. To compare variables, exponents, constant and coefficient.

3.To prevent guessing an answer.

Objectives:

1.To recall different terminologies in algebraic expression.

2. To compare variables, exponents, constant and coefficient.

3.To prevent guessing an answer.

Instruction: Match the given symbols and numbers in column A to its corresponding concepts and terminologies in column B.


A B

____1. a, b, c, x, y, z a. Algebraic Expression

____2. 2, 4, 6, 10, 20 b. Like term

____3. 5x² + y, 6x²y + 5y c. First Term

____4. ² ³ ⁴ ⁵ ⁶ ⁸ d. Term

____5. 5x² - 8x + 2 e. Literal

____6. 6x², 3x², x² f. Variable

____7. 5 is _____coefficient of x,y,z g. Exponent

____8. xy is _____coefficient of 3 h. Second term

____9. 8xy + 3mn +4hk i. Constant

____10. 3x² - 6xy + y² j. Numerical

AnswersAnswers

QuestionsQuestions

Answers

1. f2. i3. a4. g5. d6. b7. j8. e9. c10. h

Activity 3

Name: _______________________Score: ___________Date:__________Year and Section: _____________Teacher:________________________

Instruction: Identify the terms and terminologies stated in each number. Write your answer in the

space provided before the numbers.

Objectives:

1.To define different terminologies in algebraic expression.

2.To analyze the standards in answering fill in the blanks test.

3.To explore the knowledge of the students in analyzing the concepts and terminologies in algebraic expression.

Objectives:

1.To define different terminologies in algebraic expression.

2.To analyze the standards in answering fill in the blanks test.

3.To explore the knowledge of the students in analyzing the concepts and terminologies in algebraic expression.


__________1. It is a number in a given polynomials and they are real numbers in a polynomial.

__________2. It is a letter or symbol coefficient containing non-negative power or exponent.

__________3. It is a polynomial containing of only one term.

__________4. It is any letters or symbols that are used to represents of any element of a polynomial.

__________5. It is a combination of variables and constant which involved of finite numbers of indicated operation raise with a power and extract of square root.

AnswersAnswers

PreviousPrevious NextNext AnswersAnswers

__________6. It is a positive or negative integer, written in the upper right of letters or symbols.

__________7. It is polynomial contains of two terms.

__________8. It is a terms which differ only in their constant coefficient.

__________9. It is an algebraic expression involves non-negative powers or exponents containing numbers

or variables. It contains of one or more terms.

__________10. It is a polynomial contains of three terms.

Questions 1 – 5 Questions 1 – 5 Questions 6 – 10 Questions 6 – 10

Answers1.constant2.Literal coefficient3.monomial4.variable5.term6.exponent7.binomial8.Like terms9.polynomial10.trinomial

Activity 4

Name:______________________Score:_________Date:_____________Year and

Section:_________________Teacher:____________________

Instruction: Multiple Choice. Write A if the equation is monomial B if the equation is binomial

and C if the equation is trinomial.

Objectives:

1.To recognize the different terms of a polynomial.

2.To write a monomial, binomial and trinomial equation.

3.To specify if the equation is a monomial, binomial or trinomial.

Objectives:

1.To recognize the different terms of a polynomial.

2.To write a monomial, binomial and trinomial equation.

3.To specify if the equation is a monomial, binomial or trinomial.


___________1. 7x² - 9

___________2. 4xy

___________3. 6mn + 1

___________4. 86x² + 43xy + 20y

___________5. 8k³ + 6s² + 4y

___________6. 36ab

___________7. 9x² -3y + 1

___________8. 5x³ + y²

___________9. 89xy

___________10. 25x² + y

AnswersAnswers

QuestionsQuestions

Answers

1.B2.A3.B4.C5.C6.A7.C8.B9.A10.B

Activity 5Name: ______________________Score:_________Date:___________Year and Section:________________ Teacher: __________________

Instruction: Identify the polynomials in column A to its corresponding terms in column B.

Write your answer in the space provided.

Objectives:

1.To define different terms of polynomial.

2. To compare monomial to binomial, binomial to trinomial.

3.To write different equation of a polynomial in a monomial, binomial and trinomial.

Objectives:

1.To define different terms of polynomial.

2. To compare monomial to binomial, binomial to trinomial.

3.To write different equation of a polynomial in a monomial, binomial and trinomial.


A B

____1. xy a. trinomial

____2. 5x² - 8y + 2 b. three

____3. 7x² + y c. 4m + 8l

____4. Monomial d. two

____5. Binomial e. monomial

____6. Trinomial f. one

____7. Monomial contains _______ term g. polynomial

____8. Binomial contains ________ terms h. 4ab

____9. Monomial, binomial, trinomial i. 6v³ + 5x – 9

____10. Trinomial contains________ terms j. binomial

AnswersAnswers

QuestionsQuestions

Answers

1.e2.a3.j4.h5.c6.i7.f8.d9.g10.b

Activity 6 Name:____________________Score:_____________Date:____________ Year and Section:____________________Teacher: ___________________

Objectives:

1. To identify different terms of polynomials;

2. To increase proficiency in comparing monomial, binomial and trinomial; and

3. To improve the abilities in comparing monomial to binomial and binomial to trinomial.

Objectives:

1. To identify different terms of polynomials;

2. To increase proficiency in comparing monomial, binomial and trinomial; and

3. To improve the abilities in comparing monomial to binomial and binomial to trinomial.

Instruction: Identify the number of terms of the given polynomials. Write your answer in the space provided before each number.

______________1. 6x² - 8______________2. 5x² + 35xy + 25y²______________3. 9xy______________4. 8x² + 10x______________5. 7x² + 5xy + 9y²______________6. 25xy + 14y______________7. 10ab______________8. 81x² + 6xy – 14y______________9. 49x² + 16y²______________10. 36a² - 25b⁴ PreviousPrevious NextNext AnswersAnswersTABLE OF CONTEN

TSTABLE OF CONTENTS

Answers

QuestionsQuestions

1.binomial2.trinomial3.monomial4.binomial5.trinomial6.binomial7.monomial8.trinomial9.binomial10.binomial

Activity 7Name:

________________________Score:_____________Date:_____________Year and Section:___________________Teacher:

________________________

Instruction: Match the polynomial in column A to its corresponding degree in column B. Write your answer in the space provided.

A B__________1. 7x³y a. 4th degree__________2. 21a⁶b³ + 14ab² + 1 b. 6th degree__________3. 4x² c. 8th degree__________4. 7yz⁵ + 2x³y d. 1st degree__________5. 16x⁵y + 4x³y² + 2y e. 7th degree__________6. 3x f. 0 degree__________7. 3 + 5 g. 2nd degree__________8. 7m⁶n² + 3mn² + 1 j. 3rd degree__________9. 16x⁴y³ + 3y² i. 9th degree__________10. 5x³ h. 5th degree

Objectives:

1.To recall the different degrees of polynomial;

2.To have self confidence in finding the correct answers; and

3.To improve the abilities in matching an expressions to each degrees of polynomials.

Objectives:

1.To recall the different degrees of polynomial;

2.To have self confidence in finding the correct answers; and

3.To improve the abilities in matching an expressions to each degrees of polynomials.

PreviousPrevious NextNext AnswersAnswersTABLE OF CONTENTSTABLE OF CONTENTS

Answers

QuestionsQuestions

1.a2.i3.g4.h5.b6.d7.f8.j9.e10.c

Activity 8Name:_______________________Score:_____________Date:____________Year and Section:____________________Teacher:_____________________

Instruction: Identify the degree of the polynomials. Encircle the correct answer.

1. 20x⁶a³ + 10x⁴a³ - a²xa. 2nd degree b. 7th degree c. 9th degree

2. 2xyz a. 1st degree b. 2nd degree c. 3rd degree

3. 8x² - 6x³y² + 4y⁵a. 3rd degree b. 4th degree c. 5th degree

Objectives:

1.To identify degree of polynomials.

2.To select the best answer in identifying the degree of polynomial.

3.To have patient in answering multiple choice test.

Objectives:

1.To identify degree of polynomials.

2.To select the best answer in identifying the degree of polynomial.

3.To have patient in answering multiple choice test.


4. x⁵ - y⁸ a. 6th degree b. 7th degree c. 8th degree

5. 5x² + 4y⁶ a. 1st degree b. 3rd degree c. 6th degree

6. 12x³y⁸ + 6x⁶y⁴ a. 11th degree b. 10th degree c. 9th degree

7. 5x⁴y³z² a. 9th degree b. 8th degree c. 7th degree

8. 6a³ + a²b⁴ + 12a²b² + 38b⁴ a. 5th degree b. 6th degree c. 7th degree

9. xyz a. 1st degree b. 2nd degree c. 3rd degree

10. x⁶-y³

a. 7th degree b. 8th degree c. 9th degree


Answers

Questions 1 - 3Questions 1 - 3 Questions 4 - 10Questions 4 - 10

1.c2.c3.c4.c5.c6.a7. a8.b9.c10.a

Instruction: Identify the degree of the given polynomials. Write your answer in the space provided._________1. 15x⁵a + 8x⁴a⁴ - a³x_________2. 5x⁴y² - 7x⁵y⁴ + 13x²y⁵_________3. 12x³y⁸ + 24x⁶y⁴_________4. 16x⁴y³z²_________5. 5x² + 4y⁶_________6. 3a²b²c⁶+ 4a²b⁴c⁶ + 2a²b⁶c⁸_________7. 24xyz_________8. 8x² - 7x³y² +6y⁵_________9. 2a³ + a²b⁴ + 13a²b² + 38b⁴_________10. x⁵ - y⁸

Activity 9Name: __________________________Score:

_____________Date:______________Year and Section:____________________Teacher:

___________________________ Objectives:

1.To identify the degree of polynomials;

2. To write the answers correctly; and

3.To have patience in identifying the degree of polynomials.

Objectives:

1.To identify the degree of polynomials;

2. To write the answers correctly; and

3.To have patience in identifying the degree of polynomials.


Answers

QuestionsQuestions

1.8th degree2.9th degree3.11th degree4.9th degree5.6th degree6.16th degree7.3th degree8.5th degree9.6th degree10.8th degree

Post Test I

Name:__________________________Score:_____________Date:_______________

Year and Section:____________________Teacher: ___________________________

Objectives:


2. To illustrate different expressions;

3.To analyze different expressions and figure out what are the characteristics of this expression; and


Objectives:


2. To illustrate different expressions;

3.To analyze different expressions and figure out what are the characteristics of this expression; and



BB CCAA DD

A. Instruction: Identify the terms and terminologies in each number. Encircle the letter of your answer. 1. It is a letter or symbol coefficient containing nonnegative power or exponent.

a. Termsb. Coefficientc. Exponent

2. It is any letter or symbol that is used to represent any element of a given polynomial.

a. Algebraic Expressionb. Variablesc. Polynomials

3. It is a positive or negative integer, written in the upper right of letters any or symbols.

a. Exponentb. Integersc. Monomial

4. Terms which differ only in their constant coefficient is called___________.

a. Coefficientb. Literal Coefficientc. Like Terms

5. It is a polynomial containing three terms.

a. Monomialb. Binomialc. Trinomial


6. It is a number in a given polynomial.

a. Constantb. Variablec. Exponent

7. Algebraic Expression involves non-negative power or exponent containing numbers or variables.

a. Polynomialb. Numerical Coefficientc. Literal Coefficient

8. It is a number or a constant with variables and containing non-negative powers or exponents.

a. Coefficientb. Polynomialc. Variable

9. It is a factor of product of a polynomial.

a. Termsb. Degreec. Factor

10. It is a polynomial contains one term.

a. Monomialb. Binomialc. Trinomial


B. Identify the terms of the polynomials. Write R if the given polynomial is monomial, M if the given polynomial is binomial and E if it is trinomial.

______11. 4x² - 1_____12. 9x² + 25xy + 16y²_____13. 4xy_____14. 3x² + 7x_____15. x² +2xy + y²_____16. -6xy + 14y_____17. 8ab_____18. 3x² - 6xy -14y_____19. 9x² + 16y²_____20. 25a⁴ - 36b⁸_____21. 4rt_____22. 5c + k_____23. 5x² - 8x + 2_____24. 3y³_____25. 4x³ + 8y²


C. Identify the degree of polynomials. Write your answer in the space provided. __________26. 15x³a + 8x²a² - a³x__________27. 5x⁴y³ - 7x⁵y³ + 13x⁶y⁵__________28. 12x³y³ + 24x²y⁴__________29. 16x³y²z__________30. 5x² + 4y__________31. 3a²b²c⁶+ 4a²b⁴c⁶ + 2a²b⁶c⁸__________32. 24xyz__________33. 8x² - 7xy +6y__________34. 2a³ + a²b + 13ab² + 38b⁴__________35. x⁵ - y__________36.3x³__________37. 7x²y⁵__________38. 16x⁵y + 4x³y² + 2y__________39. 7m⁶ + 4x -5y__________40. 3x + 6


D. True or False. Write E if the statement is correct and R if the statement is incorrect. Write your answer in the space provided.

_____1. Algebraic expression is a combination of variables and constants which involved finite numbers._____2. In 9x², 2 is the exponent of x._____3. In 5x² - 8x + 2, 5x² is in the 1st term._____4. 4rt is a monomial_____5. In 7x²y⁵, the degree of a monomial is in the 5th degree._____6. In 4x³y², 4 is a numerical coefficient._____7. 5x² - 8x + 2 is a trinomial._____8. In 5xyz, 5x is coefficient of yz._____9. In 16x⁵y + 4x²y² + 2y, the degree of a trinomial is in 7th degree._____10. In 45c⁵g², c⁵g² is the literal coefficients


Answers

Questions DQuestions DQuestions CQuestions CQuestions BQuestions BQuestions AQuestions A

A.

1.a2.b3.a4.c5.c6.a7.a8.a9.a10.a

B.

11.M

12.E

13.R

14.M

15.E

16.M

17.R

18.E

19.M

20.M

21.R

22.M

23.E

24.R

25.M

C.

26. 4th degree

27. 11th degree

28. 6th degree

29. 6th degree

30. 2nd degree

31. 16th degree

32. 3rd degree

33. 2nd degree

34. 4th degree

35. 5th degree

36. 3rd degree

37. 7th degree

38. 6th degree

39. 6th degree

40. 1st degree

D.

1.E

2E.

3.E

4.E

5.R

6.E

7.E

8.E

9.R

10.E

Pre Test II

Name:__________________________Score:_____________ Date:____________

Year and Section:__________________Teacher: __________________________


Objectives:

1.To enhance the student’s skill in solving the algebraic expression using fundamentals operation;

2.To recall all the topics that have discuss by the teacher about solving polynomials using the fundamental operations; and

3.To have more practice in solving polynomials.

Objectives:

1.To enhance the student’s skill in solving the algebraic expression using fundamentals operation;

2.To recall all the topics that have discuss by the teacher about solving polynomials using the fundamental operations; and


INSTRUCTION: Write your solution in performing the given operations.

1. (6a² – 4b + 3c) + ( 8a² - 6b + 2c)

2. (3x – 8y + 6z) + ( 7y – 2x + 4z)

3. (5x³ + 2y²) + ( 7x³ - y²)

4. (6 – y + 3x) + (-8x + 2y + 10)

5. (7x + 4y) + (5x + 8y)

6. (5x² + 4y) + (7x² + 5y)

7. (3x³ + 4y + 4xy²) + (3x³ + 8xy² + 2y)

8. (3x + 4xy – 6y) + (4xy – 3y + 2x)

9. (8x⁵ - 3xy³ + 2y²) + (2x⁵ - 2xy³ + 2y²)

10. (5a² + 3ab + 6c) + (8a² + 3ab + 4c)

PreviousPrevious NextNext SolutionsSolutions

11. (-5x² – 4x + 2y) – (6x² - x + 3) 12. (2a³ + a² + 4a – 3) – (4a³ - 8a² + 2a + 6) 13. (16a + 9b) – (8a + 2b) 14. (-16a + 9b) – (8a – 7b) 15. (x³ - 3x² + 7x + 2) – (5x³ + x² - 10x + 24) 16. (x + y)(2x + 3y)(5x + 4y) 17. (2m2)(4m) 18. 3x3(4y2) 19. (5a + 7b – 8c)(8a + 4c) 20. (9u + 5v – 2z)(5u + 2v – 2u)


21. (88x – 44y) + (55x + 22y) 22. (37b + 49ab² - 28a³) + ( 34a³ - 32ab² - 25b) 23. (59x² + 49y) + (74x² + 54y) 24. 13x(85z) 25. (73x + 45xy – 66y) + (64xy – 93y + 82x) 26. 34m²p(86op) 27. (13x³ +14y + 24xy²) + (32x³ + 84xy² + 26y) 28. 18j²(17j⁸k⁶) 29. 14h²l⁵(-36t²) 30. 59i⁶l²(61u³v³)


31. 58xyz(34xz) 32. -14f²(62huv) 33. 28xy²(18x²) 34. 92a²b²c(57a³b²c²) 35. (x2 + 7x + 10) ÷ (x – 5) 36. (23a4b) ÷ (32c) 37. (x2 – 9x – 10) ÷ (x + 1) 38. (a3 – 1)(a – 1) 39. (12t4 – 25t3 + 18t2 + 7t – 25) ÷ (3t – 4) 40. (73x + 45xy – 66y) + (64xy – 93y + 82x)


Answers

Pre Test 31 - 40Pre Test 31 - 40Pre Test 21 - 30Pre Test 21 - 30Pre Test 11-20Pre Test 11-20Pre Test 1 - 10Pre Test 1 - 10

A.

1. 14a2 – 10b + 5c

2. x – y + 10z

3. 12x3 + y2

4. -5x + y + 16

5. 12x + 12y

6. 12x2 + 9y

7. 6x 3+ 12xy2 + 6y

8.5x + 8xy – 9y

9. 10x5 + 5xy3 + 4y2

10.13a2 + 6ab + 10c

B

11.-11x 2– 3x + 2y + 3

12. -2a3 – 7a2 + 6a + 3

13. 8a + 7b

14. -24a + 16b

15. -4x3 – 4x2 + 17x + 22

16. 10x3 + 33x2y + 35xy2 + 12y3

17. 8m3

18. 12x3y2

19. 40a2 + 56ab – 44ac + 28bc – 32c2

20. 27u2 + 33uv – 6uz + 10v 2– 4vz

C

21. 113x – 22y

22. 6a3 + 7ab2 + 12b

23. 133x2 + 103y

24. 1105xz

25. 155x + 109xy – 159y

26. 2924 m2op2

27.45x3 + 40y + 108xyz

28.306j10k6

29. -504h2l5t2

30.3599i6l3u3v3

D

31. 1972 x2yz2

32. -868 f2huv

33. 504x3y2

34. 5244a5b4c3

35. x + 10 r. 70

36. 8a4b/9C

37. x – 10

38. a4 – a 3– a + 1

39. 4t3 – 3t2 + 2t + 5 r. -5

40. 155x + 109xy – 159



___________________________Objectives:

1.To recall how to add polynomials;

2.To help the students to enhance their skills in adding two or more polynomials; and

3.To measure the capacity of the students in choosing the correct answer.

Objectives:

1.To recall how to add polynomials;

2.To help the students to enhance their skills in adding two or more polynomials; and

3.To measure the capacity of the students in choosing the correct answer.

INSTRUCTION: Choose the best answer in the box and write the letter on the space provided before the number.

a. 12x3 - y2 f. 5x + y + 16 k. 6a + 3ab + 4c p. x – y + 10zb. 12x – 12y g. –a + 3b l. 12x3 + y2 q. 12x + 12yc. 21x – 8xy + y h. 7x – 10y + 8z m. 21x + 8xy + y r. 7x + 10y + 8zd. 14a2 + 10b + 5c i. 7x – 2y + 4 n. 6a – 3ab + 4c s. 14a2 - 10b + 5ce. –x + y +10z j. a + 3b o. 7x + 2y + 4 t. -5x + y + 16


_____1. (6a² – 4b + 3c) + ( 8a² - 6b + 2c)_____2. (3x – 8y + 6z) + ( 7y – 2x + 4z)_____3. (5x³ + 2y²) + ( 7x³ - y²)_____4. (6 – y + 3x) + (-8x + 2y + 10)_____5. (7x + 4y) + (5x + 8y)_____6. (8x + 7xy + 3y) + (6x – 3xy + 4y) + (7x + 4xy – 6y)_____7. (4x + 6y + 6) + (3x – 4y – 2)_____8. (4x – 6y + 6z) + (3x – 4y +2z)_____9. (2a + ab + c) + (3c + 4a + 2ab)_____10. (2a + 4b) + ( 3a – 5b ) + ( -6a + 4b)


Answers

QuestionsQuestions

1. s2. p3. l4. t5. q6. m7. o8. h9. k10. g



___________________________Objectives:

1.To help the students to enhance their skills in adding two or more polynomials;

2.To make the students solve patiently; and

3.To show their solution clearly.

Objectives:

1.To help the students to enhance their skills in adding two or more polynomials;

2.To make the students solve patiently; and

3.To show their solution clearly.

INSTRUCTION: Write your solutions in performing the given conditions. 1. (8a² + 6ab – 2c) + (4a – 4ab + c) + (-2a + 6ab – 3c) 2. (6x² + 4xy – 8y) + (x² + xy + y) 3. (4a³ - 7ab² - 3c) + (7a³ + 6ab² + 2c) 4. (2a – ab – b) + (-3b – 4ab – 3a) + (-6b + 2ab + 4a) 5. (8x – 4y) + (5x + 2y)


AnswersAnswers

6. (3b + 4ab² - 2a³) + ( 3a³ - 3ab² - 2b) 7. (5x² + 4y) + (7x² + 5y) 8. (3x³ + 4y + 4xy²) + (3x³ + 8xy² + 2y) 9. (3x + 4xy – 6y) + (4xy – 3y + 2x) 10. (8x⁵ - 3xy³ + 2y²) + (2x⁵ - 2xy³ + 2y²) 11. (5a² + 3ab + 6c) + (8a² + 3ab + 4c) 12. (6a³ + 4ab² - 8c) + (-8c +7a³ + ab²) 13. (3m + 25n – 8) + (6n – 8 + 8m) 14. (8a + 7b) + (2a + 2c) + (5c – d) 15(5x + 2z) + (-2z + 5x)


Answers

Questions 1- 5Questions 1- 5 Questions 6 - 15Questions 6 - 15

1. 8a2 + 8ab – 4c2. 7x2 + 5xy – 7y3. 11a3 – ab2 – c 4. 3a – 3ab – 10b 5. 13x – 2y6. a3 + ab2 + b7. 12x2 + 9y8. 6x3 + 12xy2 +6y9. 8xy – 2y 10. 10x5 – 5xy3 + 4y2

11. 13a2 + 6ab + 10c12. 13a3 + 5ab2 – 16c13. 11m + 31n - 1614. 10a + 7b + 7c – d 15. 10x



___________________________ Objectives:

1.To have more practice in adding polynomials;

2.To enhance the students’ ability in evaluating expression; and

3.To practice the students in subtracting polynomials mentally.

Objectives:

1.To have more practice in adding polynomials;

2.To enhance the students’ ability in evaluating expression; and

3.To practice the students in subtracting polynomials mentally.

INSTRUCTION: Fill in the blanks to make the statement correct. 1. (9y2 + 2x – 3y) + ___________________ = 11y2 – 5x + y2. (11t + 3x – 4u) + (-8x + 2u + 2t) = ___________________3. (6a3 + 4ab2 – 8c) + ___________________ = 13a3 + 5ab2 – 16c4. (8a2 + 3ab – 4c) + ____________________ = 2a2 + 7ab – 6c 5. _______________ + (-4a + 5x) = -6a + 7x6. (5t2 + 2t – 3y) + __________________+ ________________ = 29t2 - 4t + y7. _______________ + (-4a3 + 3b2 – 4c) + _________________ = -12a3 – 14b2 + 88. _________________ + __________________ + (11je + 18r2 – 25x3) = -15je + 2r2 – 5x3

9. _________________ + (8g3 – 6) + (g3 + 5) = 5g3 - 11 10.__________________ + __________________ = 11h3 – 8x

AnswersAnswersPreviousPrevious NextNextTABLE OF CONTENTSTABLE OF CONTENTS

Answers

QuestionsQuestions

1. 2y2 – 7x + 4y2. 13t – 5x – 2u 3. 7a3 + ab2 – 8c4. -6a + 4ab – 2c 5. -2a + 2x6. 12t2 + 2t – y and 12t2 – 8t + 5y7. -4a3 – 12b2 – 2c and -4a3 – 5b2 - 2c 8. -20je – 8r2 + 10x3 and -6je – 8r2 + 10x3

9. -4g3 + 1210. 5h3 – 4x and 6h3 -4x



___________________________Objectives:

1.To help the students to enhance their skills in subtracting two or more polynomials;

2.To become more efficient in subtracting polynomials; and

3.To show clearly their own solution.

Objectives:


2.To become more efficient in subtracting polynomials; and

3.To show clearly their own solution.

INSTRUCTION: Perform the indicated operation and show your solution. 1.Subtract 4x² - 5x + 7 to x – 8 2.Subtract 3a² - 4a + 3 to a + 53.Subtract 4a – 8b + 3c to 12a + 6b – 4c4.(2a + 2b + 2c) – (6a – 3b + c)5.(-5x² – 4x + 2y) – (6x² - x + 3)6.(2a³ + a² + 4a – 3) – (4a³ - 8a² + 2a + 6)7.(16a + 9b) – (8a + 2b)8.(-16a + 9b) – (8a – 7b)9.(x³ - 3x² + 7x + 2) – (5x³ + x² - 10x + 24) 10.(3x 4 +4x 3 -5x 2 +18) - (7x 5 +3x 4 -12x 3 -3x 2 + 7x - 9)


AnswersAnswers

Answers

QuestionsQuestions

1. 4x2 – 6x + 152. 3a2 – 5a – 2 3. -8a – 14b + 7c4. -4a + 5b + c5. -11x2 – 3x + 2y – 3 6. -2a3 + 7a2 + 2a – 9 7. 8a + 7b8. -24a + 16b9. -4x3 – 4x2 + 17x – 22 10. -7x5 + 16x3 – 2x2 + 27



___________________________Objectives:


2.To avoid guessing the answer; and

3.To make the students read the instruction clearly and thoroughly.

Objectives:



3.To make the students read the instruction clearly and thoroughly.

INSTRUCTION: Draw a positive sign if the statement is correct and negative sign if the statement is incorrect in the space provided. ___________ 1. (3x + 2y + 2z) – (6x – 5y + 3z) is equal to -3x + 7y + z.___________ 2. In equation, (7x³ +2y² + 2z) – (-5x³ + 4y² - 6z) the second term of each polynomials

have the difference of -2y2.___________ 3. (3x – 9y + 4z) – (-3x – 6y + 9z) is equal to 6x – 3y -5z.___________ 4. In (9x⁶ + 6y⁵) – (3x⁶ - 5y⁵) the exponent of the difference is in the fifth degree.___________ 5. (9a + 7b + 4c) – (8a + 7b + 2c) is equal to a +2c.


AnswersAnswers

___________ 6. (-5x + 7y – z) – (6x – 7y + 2z) is equal to 11x + 14y – 3z.

___________ 7. In equation (-11x³ - 5x² - 7x -6) – (-9x³ - 6x² + 9x + 3) the third term is16x.

___________ 8. The difference of 16xy – 7xy is 9xy.

___________ 9. In (-4x³ + 6y² - 3z) – (-5x³ - 3y² - 2z), the second equation will become positive.

___________ 10.The difference of 3ab – 7ab is a positive.

AnswersAnswersPreviousPrevious NextNext

Answers


1. +2. +3. +4. -5. +6. -7. +8. +9. +10. -



___________________________Objectives:

1.To make the students think fast;

2.To help the students elaborate the expressions of a polynomials; and

3.To enhance their skills in subtracting polynomials.

Objectives:

1.To make the students think fast;

2.To help the students elaborate the expressions of a polynomials; and

3.To enhance their skills in subtracting polynomials.

INSTRUCTION: Fill in the blanks to make the statement correct. 1.(9l2 + 4m – 9y) - _____________ = 10l2 – 5m + y2.(4t + 3x – 4u) - (-5x + 2u + 2t) = _________________3.(6a3 + 4ab2 – 8c) - _________________ = 3a3 + 5ab2 – 16c4.(8a2 + 3ab – 4c) - _________________ = 2a2 + 4ab – 6c 5._________________ - (-4a + 5x) = -6a + 7x6.(5t2 + 2t – 3y) + _________________ = 29t2 - 4t + y7._________________ - (-4a3 + 3b2 – 4c) = -12a3 – 14b2 + 88._________________ - _________________ = -15je + 2r2 – 5x3

9._________________ - (8g3 – 6) - (g3 + 5) = 5g3 – 1110.______________- _______________= 11h3 – 8x


AnswersAnswers

Answers

QuestionsQuestions

1. –l2 + 9m + 10y 2. 8x + 2t – 6u 3. 3a3 – ab2 + 8c4. 6a2 – ab + 2c5. -10a + 12x6. 24t2 – 6t + 4y7. -16a3– 11b2 + 4c8. 15je + 3r 2– 2x3 and 30je + r2 + 3x3

9. 12g3 + 1010. 16h3 – 3x and 5h3 + 5x



___________________________ Objectives:

1.To be more efficient in multiplying monomials;

2.To help the students to enhance their skills in multiplying monomials; and

3.To recall different laws in multiplying monomials.

Objectives:

1.To be more efficient in multiplying monomials;

2.To help the students to enhance their skills in multiplying monomials; and

3.To recall different laws in multiplying monomials.

INSTRUCTION: Write your solutions in performing the given operations. 1. (4xy - 2)(5y – 3z2)2. -3a(3a⁴b³c²d + 3b)3. (-4b-c)(3c + 8)4. 2x(3x³)5. 8u(2u³v²w)6. (x + y)(2x + 3y)(5x + 4y)7. (2m2)(4m)


AnswersAnswers

8. 3x3(4y2)

9. (5a + 7b – 8c)(8a + 4c)

10. (9u + 5v – 2z)(5u + 2v – 2u) 11. (-5x2y3w)(2x + y) 12. (4x + 2y)(5x3 + 2x2 – y) 13. (6a3 + b2)(4a3

+ b – y) 14. (2t2 + 3t)(4t2

– 3t2 –t) 15. (4x2 – y3)( 4x3 – y2 + 6)


Answers

Questions 1 - 7Questions 1 - 7 Questions 8- 15Questions 8- 15

1. 20xy2 – 10y – 8xyz2 – 6z2

2. -9a5b3cd2 – 9ab3. -12bc – 3c2 – 32b – 8c4. 6x4

5. 16u2v2w6. 10x3 + 35x2y + 35xy2 + 12y3

7. 8m3

8. 12x3y2

9. 40a2 + 56ab – 44ac + 28bc – 32c2

10. 27u2 + 33uv – 6uz +10x2 – 4vz11. -10x3y3w – 5x2y2w 12. 20x4 + 8x3 – 4xy + 10x3y + 4x2y – 2y2 13. 24a5 + 6a3b – 6a3y + 4a3b + b3 – b2y 14. 4t4 + t3 -3t2

15. 16x5 – 4x2y + 24x2 – 4x3y3 + y5 – 6y3



___________________________ Objectives:

1.To have more attention in doing activity;

2.To make the students enjoy answering the puzzle; and

3.To enhance their skills in multiplying monomials.

Objectives:

1.To have more attention in doing activity;

2.To make the students enjoy answering the puzzle; and

3.To enhance their skills in multiplying monomials.

INSTRUCTION: Solve the cross-word puzzle by performing the indicated operations in the given expressions and show your solutions in the given box.

1. 2. 3.

4.

7.

5. 6.

8.

9.


AnswersAnswers

Across1. (2xy)(9x²)(7y)4. (5u²)(5u)5. (9w)(5)7. (zmn)(z³m²n)8 (3x²)(3x²y)9. (26a²)(2a²)

Down 1. (6u²)(3u)2. 2(19)(3)3. (yzw)(yz)4. 2m³z² (m²z²)6. 2(7)(3)8. 3a²(8a)(4a)

PreviousPrevious NextNext

Answers

Questions Questions

Across

1. 126x3y2

4. 25u3

5. 45w7. z4m3n2

8. 9x4y9. 52a2

Down

1. 18u3

2. 1143. y2z2w4. 2m4z4

6. 428. 96a4



___________________________Objectives:

1.To enhance their thinking in multiplying monomials mentally;


3.To make the students more accurate their answers.

Objectives:

1.To enhance their thinking in multiplying monomials mentally;


3.To make the students more accurate their answers.

INSTRUCTION: Match column A with column B. Write the correct letter before the number. A B

_____1. 3x²(15xy) a1. 16x3y2

_____2. 4c² (2t) a7. 7uvxyz_____3. 19x(3xy) a3. -24h2l5t2

_____4. m²p(op) a4.45x3y_____5. 3x(5z) b5.20x2yz2

_____6. 8j²(j⁸k⁶) b2. 14a5b4c3

_____7. 4h²l⁵(-6t²) b6. 140xyz


AnswersAnswers

_____8. 9i⁶l²(6u³v³) c5. 8c2t_____9. 5xyz (4xz) c6. m2op2

_____10. -14f²(6huv) d1. 8j10k6

_____11. 2xy² (8x²) d2. -84f2huv_____12. 2a²b²c (7a³b²c²) e8.288c3n2

_____13. 5x (4y)(7z) f7. 57x2y_____14. 7uv (xyz) g5.54 i6l2 u³v³_____15. 24c (-12n²)(-c²) h8. 15


Answers


1. a42. c53. f74. c65. h86. d17. a38. g59. b510. d211. a112. b213. b614. a715. e8



___________________________ Objectives:

1.To recall how to divide polynomials.

2.To enhance the students’ skill in dividing polynomials.

3.To be more patient in dividing polynomials.

Objectives:

1.To recall how to divide polynomials.

2.To enhance the students’ skill in dividing polynomials.

3.To be more patient in dividing polynomials.

INSTRUCTION: Divide the following polynomials. Show your solution and encircle your answer. 1.(x²-25) ÷ (x+5)2.(6y² + y – 5) ÷ (6y-5)3.4 a²b² ÷ a²b²4.(x4 – 3x2 + 2x) ÷ (x-1)5.(x2 + 7x + 10) ÷ (x – 5) 6.(23a4b) ÷ (32c)7.(x2 – 9x – 10) ÷ (x + 1)8.(a3 – 1)(a – 1)9.(12t4 – 25t3 + 18t2 + 7t – 25) ÷ (3t – 4)10.(56v2

- 5x2 - 27vx) ÷ (7v + x)


AnswersAnswers

Answers

Questions Questions

1. x – 5 2. y + 13. 44. x5. X + 12 r. 706. 8a4b/9c7. x – 10 8. a + 19. 4t3 – 3t2 + 2t + 5 r. -510. 8v – 5x



___________________________Objectives:

1.To enhance the students’ skill in dividing polynomials;

2.To help the students to be more familiar in dividing polynomials using the long method; and

3.To have confidence in dividing polynomials.

Objectives:

1.To enhance the students’ skill in dividing polynomials;

2.To help the students to be more familiar in dividing polynomials using the long method; and

3.To have confidence in dividing polynomials.

INSTRUCTION: Perform the indicated operations.

1. (x11) ÷ (x4)2. (-44x) ÷ (53x) 3. (x8) ÷ (x3)4. (16m2 – 25m2) ÷ (4m + 5m)5. (5x3 – 14x + 3) ÷ (x-2)6. (3x3 – 4x2y + 5xy2 + 6y3) ÷ (x2- 2xy +3y2)7. (9xy2 – 6x3) ÷ (3x)


AnswersAnswers

8. (2a2b2) ÷ (a2b2)

9. (4x2y3 – 24xy4) ÷ (2xy2)

10. (12x3y4 + 18x4y2 – 36xy3) ÷ (3x2y2)

11. (7x³y² - 14x⁵y³ + 28x⁸y⁵ - 21x⁵y⁶) ÷ (7x³y²)

12. 4e² ÷ 2e

13. (2y² – 5y – 6) ÷ (2y – 1)

14. (2x²- 5x – 12) ÷ (2x + 3)

15. (3an + bm) ÷ (anbm)


Answers

Questions 1 - 7Questions 1 - 7 Questions 8- 15Questions 8- 15



___________________________ Objectives:

1.To help the students to recall the laws of exponent and signs in dividing polynomials;

2.To make the students be familiar in the instructions given; and

3.To read the instruction carefully and thoroughly.

Objectives:

1.To help the students to recall the laws of exponent and signs in dividing polynomials;

2.To make the students be familiar in the instructions given; and

3.To read the instruction carefully and thoroughly.

INSTRUCTION: Do what the statement says. Always show your solutions.

1.Divide 10m3 – 2m2 + 6m – 4 by m2 – m + 1. 2.If we divide the trinomial 14f2 + 18f – 12 by 12f – 3 what will be the quotient? Box your answer.3.Divide x2 – 10x + 7 by x + 2.4.What is the second term in the quotient of 2p4 – p2 – 5 by p2 – 1?5.What is the sign of the third term in the quotient of 4n2 + n – 6n3 + 3 by 3n2

+ 5?6.Divide 2x2 – 5x – 6 by 2x – 1.7.Find the quotient of 3a5 + a4b – 3ab4 – b5 by 3a + b. Encircle your answer.8.What is the quotient of –u4

+ 2u3 + u2 + 4 by u + 2?9.What is the third term in the quotient of y3

– 1 by y – 1?10.Divide a7 + a2 – 2a + 7a6 + a5 – 2a4

+ 1 by a – 2. Box your answer and encircle the fifth term of the quotient.


AnswersAnswers

Answers

Questions Questions

Post Test IIName: __________________________Score:


___________________________

Objectives:

1.To enhance the student’s skill in solving the algebraic expression using fundamentals operation.

2.To recall all the topics that have discuss by the teacher about solving polynomials using the fundamental operations.


Objectives:

1.To enhance the student’s skill in solving the algebraic expression using fundamentals operation.

2.To recall all the topics that have discuss by the teacher about solving polynomials using the fundamental operations.



INSTRUCTION: Perform the indicated operations and show your solutions.

A.Add the following Algebraic Expressions.

1.(10a² + 5ab – 3c) + (23a – 15ab + 20c) + (-28a + 16ab – 13c)

2.(26x² + 24xy – 18y) + (2x² + 2xy + 2y)

3.(41a³ - 75ab² - 38c) + (76a³ + 67ab² + 29c)

4.(28a – 2ab – 4b) + (-38b – 46ab – 32a) + (-69b + 22ab + 49a)

5.(88x – 44y) + (55x + 22y)

6.(37b + 49ab² - 28a³) + ( 34a³ - 32ab² - 25b)

7.(59x² + 49y) + (74x² + 54y)

8.(13x³ +14y + 24xy²) + (32x³ + 84xy² + 26y)

9.(73x + 45xy – 66y) + (64xy – 93y + 82x)

10.(18x⁵ - 13xy³ + 12y²) + (12x⁵ - 12xy³ + 12y²)


B. Subtract the following Algebraic Expressions.

1.(33x + 12y + 27z) – (46x – 15y + 23z)

2.(97x³ +42y² + 52z) – (-51x³ + 48y² - 66z)

3.(13x –19y + 14z) – (-13x – 16y + 19z)

4.(91x⁶ + 61y⁵) – (31x⁶ - 51y⁵)

5.(92a + 72b + 42c) – (82a + 72b + 22c)

6.(-35x + 73y – 3z) – (63x – 37y + 23z)

7.(-11x³ - 54x² -47x -64) – (-49x³ - 64x² + 49x + 43)

8.16xy – 72xy

9.(-48x³ + 86y² - 38z) – (-85x³ - 38y² - 82z)

10.39ab – 97ab


C. Multiply the following Algebraic Expressions.

11. 6x²(25xy)

12. 42c²(21t)

13. 19x(36xy)

14. 34m²p(86op)

15. 13x(85z)

16. 18j²(17j⁸k⁶)

17. 14h²l⁵(-36t²)

18. 59i⁶l²(61u³v³)

19. 58xyz(34xz)

20. -14f²(62huv)

21. 28xy²(18x²)

22. 92a²b²c(57a³b²c²)

23. 51x(14y)(71z)

24. 76uv(23xyz)

25. 24c(-125n²)(-96c²)


D. Divide the following Algebraic Expressions.

26. (x⁵) ÷ (x²)

27. (-4²x) ÷ (2³x)

28. (16x8) ÷ (4x3)

29. (10m2 – 4m2) ÷ (3m + 3m)

30. (10x3 – 24x + 6) ÷ (x-4)

31. (23x3 – 44x2y + 65xy2 + 62y3) ÷ (6x2- 12xy +24y2)

32. (90xy2 – 60x3) ÷ (10x)

33. (12a2b2) ÷ (6a2b2)

34. (14x2y3 – 24xy4) ÷ (5xy2)

35. (12x3y4 + 18x4y2 – 36xy3) ÷ (12x2y2)

36. (28x³y² - 14x⁵y³ + 35x⁸y⁵ - 21x⁵y⁶) ÷ (7x³y²)

37. 20e² ÷ 4e

38. (2y² – 5y – 6) ÷ (2y – 1)

39. (22x²- 16x – 12) ÷ (4x + 6)

40. (21an + bm) ÷ (7anb)


Answers

Post Test APost Test A

A.

1. 10a2 + 5a + 6ab + 4c2. 28x2 + 26xy – 16y 3. 117a3 – 8ab2 – 9c4. 45a – 36ab – 111b 5. 143x – 22y6. 6a3 + 17ab2 + 8b7. 133x2 + 103y8. 45x3 + 108xy2 + 40y9. 155x + 109xy – 159y10. 30x5 – 25xy3 + 24y2

Answers

Post Test BPost Test B

B.

1. -13x – 3y + 50z

2. 148x3 – 6y2 + 118z

3. 26x – 3y – 5z

4. 60x 6+ 112y

5. 10a + 20c

6. 28x + 110y – 26z

7. 38x 3+ 10x2 + 96x - 107

8. -56xy

9. 37x 3+ 124y2 + 44z

10. -58ab

Answers

Post Test CPost Test C

11. 150x3y

12.882c2t

13. 684x2y

14. 2924m2op2

15. 1105xz

16.306j10k2

17. -504h2l5t2

18. 5599i6l2u3v3

19. 1972x2yz2

20. -868f2huv

21.504x3y2

22. 5244a5b4c3

23. 50694xyz

24. 1748 vxyz

25. 288,oooc3n3

Answers

Post Test DPost Test D

Pre Test III

Name:__________________________Score:_____________Date:_____________

Year and Section:__________________Teacher: ___________________________

Objectives:

1.To recall all the ways in getting the special products of the polynomial;

2.To have more practice solving polynomials; and

3.To be more efficient in solving polynomials with their special products.

Objectives:

1.To recall all the ways in getting the special products of the polynomial;

2.To have more practice solving polynomials; and



INSTRUCTION: Solve the “SPECIAL PRODUCTS” of the following equations. Show your solution and box your final answer.

1.(f2 _ 2c) 2

2.(x + 13) 2

3.(16a2 + b) 2

4.(2p + 2q) 2

5.(2am +3z) 2

6.(9y2 + 5xy) 2

7.(27hx + 6og) 2

8.(a – 4) (a + 6)

9.(x – 9) (x + 3)

10.(m + 8) (m + 5)


11. (f +2) (f – 8)

12. (w + 4) (w + 11)

13. (s + 5) (s + 6)

14. (c + 10) (c – 3)

15. (a + 8) (a + 9)

16. (i + 25) (i – 3)

17. (i + 25) (i – 3)

18. (m + 5) (m – 6)

19. (h + 3) (h + 5)

20. (l + 6) (l + 9)


21. (ax – 2xy) 3

22. (xy2 + wz2) 3

23. (7x2+ y4) 3

24.(2a + 5b)2

25.(11a3 + 4x2) 2

26.(2x + 6) 2

27.(-6xy2)2(5x2 – 6y4 + 7x)

28.ax (9x2 + ay2 + a2y)

29.7ab (cd2-9ab –cd3)

30.x3(3x2 + 4x – 6 )

31.4xy (12x2 + 4x + 12y)

32.x3(5x2 + 10x + 5)

33.(x4y2) 2

34.(a2ceem) 2

35.(21t3w3) 2


Answers

1. f⁴ - 4fc² + 4c²2. x² + 26x + 1693. 256a4 + 32a2 + b2

4. 4p2 + 8pq + 4q2

5. 4a2m + 12am z + 9q2

6. 81y4 + 90xy3 + 25x2y2

7. 279h2x + 324hx 0g + 360g

8. a2 + 2a - 249. x2 – 6x - 2710. m2 + 13m + 40

11. f2 – 6f - 16

12. w2 + 15w + 44

13. s2 + 11s + 30

14. c2 + 7c - 30

15. a2 + 17a + 72

16. i2 + 21i - 75

17. i2 + 21i - 75

18. m2 – m - 30

19. h2 + 8h + 15

20. l2 + 15l + 54

21. a3x2 – 6a2x3y – 12ax3y 2 – 8x3 y3

22. x3y6 + 3x2y3wz2 + 3xy3w2y4 + w3z6

23. 1029x6 + 147x4y4 + 21x2y8 + y12

24. 4a2 + 20ab + 25b2

25. 121a6 + 88a3x2 + 64x4

26. 4x2 + 24x + 36

27. 180x4y4 -216x2y8 + 252x3y4

28. 9ax3 + a2xy2 + a3xy

29. 7abcd2 – 63a2b2 – 9abcd3

30. 3x5 + 4x4 – 6x3

31. 48x3y + 16x2y + 48xy2

32. 5x5 + 10x4 + 5x3

33. x8y4

34. a4c2ee2m

35. 441t6 w6

Pre Test 21 - 35Pre Test 21 - 35Pre Test 11-20Pre Test 11-20Pre Test 1 - 10Pre Test 1 - 10



___________________________ Objectives:

1.To recall how to square polynomials;

2.To enhance the student’s skill in squaring monomials; and

3.To have more practice in squaring polynomials.

Objectives:

1.To recall how to square polynomials;

2.To enhance the student’s skill in squaring monomials; and

3.To have more practice in squaring polynomials.

INSTRUCTION: Square the following monomials. Encircle your answers.

1.(5x)2

2.(4y3) 2

3.(x4y2) 2

4.(a2ceem) 2

5.(k10m3n) 2 6.(4jnhx+1)2

7.(10m)2

8.(4xyz2) 2

9.(25mn) 2

10.(2x2+n) 2


AnswersAnswers

Answers

1. 252x

2. 16y6

3. x8y4

4. a4c2ee2m

5. k20 m6n

6. 16j2nh2x+2

7. 100m2

8. 16x2y2z2

9. 625m2n

10. 44 + 2n

Questions Questions



___________________________Objectives:1.To enhance the student’s skill in squaring monomials.2.To make the students be accurate with their answer.3.To have the students some curiosity.

Objectives:1.To enhance the student’s skill in squaring monomials.2.To make the students be accurate with their answer.3.To have the students some curiosity.

INSTRUCTION: Answer the riddle below and show your solution. It is a letter or symbol that is used to represents any elements of a given polynomials.

81x4y2 x2y4 36x2y4 225x4y2 x2y4 81x2ay2b 225x2y2 81x4ay6b 36x6y2

S = (6x3y)2 A = (xy2) I = (15x2y) R = (6XY2) E = (9x2ay3b)

B = (9xayb) L = (15xy) V = (9x2y)

Name: __________________________Score: _____________Date:______________

Year and Section:____________________Teacher: ___________________________


AnswersAnswers

Answers

1. V2. A3. R4. I5. A6. B7. L8. E9. S

Questions Questions



___________________________Objectives:

1.To enhance the student’s skill in squaring monomials.

2.To be more efficient in squaring monomials.

3.To have more practice in squaring monomials

Objectives:

1.To enhance the student’s skill in squaring monomials.

2.To be more efficient in squaring monomials.

3.To have more practice in squaring monomials

INSTRUCTION: Solve the following monomials and box your answer. 1. (7x3) 2

2. (uv2) 2

3. (10x) 2

4. (8y) 2

5. (xy) 2

6. (6m6x) 2

7. (13axb2yc5z) 2


AnswersAnswers

8. (3a4b3) 2

9. (53x2) 2

10. (13x2y2) 2

11. (4nx+1) 2

12. (5ab3) 2

13. (21t3w3) 2

14. (3ba+2m2w2) 2

15. (8love) 2


Answers1. 49x6

2. u2v4

3. 100x2

4. 64y2

5.x2y2

6. 36m12x

7. 169a2xb4yc10z

8. 9a8b6

9. 2809x4

10. 169x4y4

11. 8n2x + 2n

12. 25a2b6

13. 441t6w6

14. 9b2a+4 m4w4

15. 64l20v2e




___________________________Objectives:

1.To help the students to avoid guessing the answer.

2.To make the students follow the instruction carefully.

3.To have more practice in multiplying monomials.

Objectives:

1.To help the students to avoid guessing the answer.

2.To make the students follow the instruction carefully.

3.To have more practice in multiplying monomials.

INSTRUCTION: Write capital A if the statement is true and small letter a if the statement is false. Show your solution if it is needed. __________1. In equation 3x2(9x2 + 3x -4), the third of the product is positive 12x2. __________2. ab(a + b +c ) have the product of a2b + ab2 + abc. __________3. The equation 3bc ( 2a + 3b + 4c + 3d) have the product of trinomial. __________4. The equation x2y2(xy + xy2 + 3xy) is multiplying monomial by trinomial. __________5. In this equation 4bc(a2bc + a2b2c + 3bc) the product is in the sixth degree.


AnswersAnswers

__________6. The product of the third term of the equation 4c(5a2 + 2c2 – 5d + 3b) is -20cd. __________7. In 2x + 1(4x+1 + yx), the first term of the product has an exponent of 2x. __________8. 3(4x + 2y + 3x2 – y2) have the product of 9x2 – 3y2 + 12x +6y. __________9. In 45x2y2z2(2 x2y2 – 4x2y – 3yz2) the third term of the product is 135x2y3z4. Show your solution in the given space and encircle the third term of the product.

________10. 5j2(10ex + 2r2 – 14i2 + 13cx) have the product of 50ej2x + 10j2r2 + 70i2j2 + 65cx.


Answers

1. a2. A3. a4. A5. a6. A7. a8. A9. a10. a

Questions 1 - 5 Questions 1 - 5 Questions 6 - 10 Questions 6 - 10



___________________________ Objectives:

1.To help the students to enhance their skills in multiplying monomials by polynomials faster;

2.To have more practice in multiplying monomials; and

3.To show their solution clearly and thoroughly.

Objectives:

1.To help the students to enhance their skills in multiplying monomials by polynomials faster;

2.To have more practice in multiplying monomials; and

3.To show their solution clearly and thoroughly.

INSTRUCTION: Perform the indicated operations. Show your solutions and box your answers.

1. x(y2 + x2y + 6)2. a (4a2 – 7a – 2)3. 2x(3x2 + 4x + 9)4. 2r(3rst + 30r2t + 3s)5. abc( ab – a + b – 3)6. ax (9x2 + ay2 + a2y)7. 7ab (cd2-9ab –cd3)8. x3(3x2 + 4x – 6 )9. 4xy (12x2 + 4x + 12y)10. x3(5x2 + 10x + 5)


AnswersAnswers

Answers

1. xy2 + x3y + 6x2. 4a3 – 7a2 – 2a3. 6x3 + 8x2 + 18x4. 6r2st + 60r3t5. a2b2c – a2bc + ab2c – 3abc6. 9ax3 + a2xy2 + a3xy7. 7abcd2 – 63a2b2 – 7abcd3

8. 3x5 + 12x4 – 6x3

9. 48x3y + 16x2y + 48xy2

10. 5x5 + 10x4 + 5x3

Questions Questions



___________________________ Objectives:

1.To make the students practice in more equation.

2.To be more accurate with their answer.

3.To have more patient in solving an equation.

Objectives:

1.To make the students practice in more equation.

2.To be more accurate with their answer.


INSTRUCTION: Perform the following equation in the indicated operation and show your solution. Make your answer inside the box.

1. 14x2(4xy2 + 27x +x4‑ ) 5. -7h(4g2 + 7y – 6r)

2. 2y(y2

+ 4y – 21 ) 6. 8x(5t2 + 3x3 – 5) 3. 21dp (3d2 + 9d) 7. (-6xy2)2(5x2

– 6y4 + 7x) 4. 15p2q(48pq – x2) 8. 11e3j2(6e2x + 2j2r – 6)


AnswersAnswers

Answers

1. 56x3y2 + 378x3 + 14x6

2. 2y3 + 8y2 - 423. 63d3p + 189d2p4. 720p3q2 – 15 p2qx2

5. -28q2h – 49hy + 42hr6. 40t2x + 24x3x – 40x

7. 180x4y4 – 216x2y8 + 252x3y4

8. 66e6xj2 + 22e3j4t – 66e3j2

Questions Questions



___________________________Objectives:

1.To recall how to square a binomial;

2.To help the students to square a binomial; and

3.To enhance the skills of the students in squaring binomial.

Objectives:

1.To recall how to square a binomial;

2.To help the students to square a binomial; and

3.To enhance the skills of the students in squaring binomial.

INSTRUCTION: Square the following binomials and show your complete solutions. Box your answers.

1.(4a +b)2

2.(2x + 3y) 2

3.(4u + 3v) 2

4.(8a + 3u) 2

5.(5a – b) 2

6.(2a + 5b)2

7.(5t2 + 5d)2

8.(12e3 – j4) 2

9.4y2 + 4z3) 2

10.(11a3 + 4x2) 2


AnswersAnswers

Answers

1. 16a2 + 8ab + b2

2. 4x2 + 12xy + 9y2

3. 16u2 + 24uv + 9v2

4. 64a2 + 48au + 9u2

5. 25a2 – 10 ab + b2

6. 4a2 + 20 ab + 25b2

7. 25t4 + 50dt2 + 25d2

8. 144e6 – 24e3j4 +j8

9. 16y4 + 32y2z3 + 16z6

10. 121a6 + 88a3 + 16x4

Questions Questions



___________________________ Objectives:

1.To help the students to enhance their skills in squaring binomial.

2.To show their solution accurately.

3.To have confidence in squaring binomial.

Objectives:

1.To help the students to enhance their skills in squaring binomial.

2.To show their solution accurately.

3.To have confidence in squaring binomial.

INSTRUCTION: Square the following binomials. Show your solution and encircle your answer.

1.(y – 9)2

2.(2x + 6) 2

3.(x2 + 1) 2

4.(y2 _ 4y) 2

5.(x + 3) 2

6.(3b2 + b) 2

7.(2x + 1) 2


AnswersAnswers

8. (2x -3y) 2

9. (2x2 + 6x) 2

10. (27x2 + y) 2

11. (y2 – 13y) 2

12. (x2 + 4) 2

13. (2x – 10) 2

14. (2x + 8) 2

15. (x3 – 4x) 2


Answers

1. y3 – 18y +81 2. 4x3 + 24x +363. x4 + 2x2 + 14. y4 – 8y3 + 16y2

5. x2 + 6x + 96. 9b4 + 6b3 + b2

7. 4x2 4x + 18. 4x2 – 12xy + 9y2

9. 4x4 + 24x3 + 36x10. 729x4 + 54x2y + y4

11. y4 – 26y3 – 169y2

12. x4 + 8x2 + 16x13. 4x2 – 40x + 10014. 4x2 + 32x + 6415. x6 – 844 + 16x2

Questions 1 – 7 Questions 1 – 7 Questions 8 - 15 Questions 8 - 15



___________________________Objectives:

1. To help the students to enhance their skills in squaring binomial.

2. To have the student a mastery in squaring binomial.

3. To have more patient in squaring a binomial.

Objectives:

1. To help the students to enhance their skills in squaring binomial.

2. To have the student a mastery in squaring binomial.

3. To have more patient in squaring a binomial.

INSTRUCTION: Solve the following binomial and show your complete solution. Encircle your answer. 1. (5y – 1) 2 6. (5a3 + x2) 2

2. (2c + d) 2 7. (y – 2) 2

3. (x2 + 2y) 2 8. (2xy – 4x) 2

4. (5at – 1) 2 9. (8x – 2 ) 2

5. (3x2 + 2x2) 2 10. (3x2 + 2y) 2


AnswersAnswers

Answers

1. 25y2 – 10y + 12. 4c2 + 4cd + d2

3. x4 + 4x2y + 4y2

4. 25a2t2 – 10at + 15. 9x4 +12x4 + 4x4 or 25x4

6. 25a6 + 10a3x2 + x4

7. y2 – 4y + 48. 4x2y2 – 16x3y – 16x3

9. 64x2 – 32x + 410. 9x4 + 12x2y + 4y2

Questions Questions



___________________________ Objectives:

1.To help the students to enhance their skills in cubing binomial.

2.To have the student a mastery in cubing binomial.

3.To have some confidence in cubing binomial.

Objectives:

1.To help the students to enhance their skills in cubing binomial.


3.To have some confidence in cubing binomial.

INSTRUCTION: Solve the following binomial. Show your complete solution and box your answer.

1.(x + y)3

2. (2x + 4y) 3

3.(3x3 + 5y) 3

4. (x – y) 3

5.(4a – 2y) 3

6.(7m + 3n) 3

7.(8b + 4y) 3

PreviousPrevious NextNextTABLE OF CONTEN

TSTABLE OF CONTENTS

AnswersAnswers

8. (12c2 – 6x2) 3

9. (3b3 – 7y) 3

10. (6e2 + 3j) 3

11. (9a3 – 7m) 3

12. (4d2 + 3f) 3

13. (3q2 – 4k) 3

14. (6k2 – 5y) 3

15. (8x – 12y) 3


Answers

1. x3 + 3x2y + 3xy2 + y3

2. 8x3 + 48x2y + 96xy2 + 64y3

3. 27x9 + 135x6y + 225x3y2 + 125y3 4. x3 - 3x2y + 3xy2 – y3

5. 64a3 – 96a2y + 48ay2 – 8y3

6. 343m3 + 441m2n + 189mn2 + 27n3

7. 512b2 + 768b2y + 384by2 + 64y3

8. 1728c6 – 2592c4x2 + 1296c2x4 – 216x6

9. 27b9 – 189b6y + 441b3y2 – 343y3

10. 216e6 + 324e4j + 162e2j2 + 27j3

11. 729a9 – 1701a6m + 1323a3m2 – 343m3

12. 64d6 + 144d4f + 108d2f2 + 27f3

13. 27q6 – 108q4k + 144k2q – 64k3

14. 216k6 – 540k4y + 450k2y2 - 125y3

15. 512x3 – 2304x2y + 3456xy2 – 1728y3

Questions 1 - 7 Questions 1 - 7 Questions 8 - 15Questions 8 - 15



___________________________Objectives:

1.To recall how to cube binomials.

2.To show complete solution clearly.

3.To have a confidence in cubing binomials.

Objectives:

1.To recall how to cube binomials.

2.To show complete solution clearly.

3.To have a confidence in cubing binomials.

INSTRUCTION: Solve the following binomial. Show your complete solution. Box your answer.

1.(2x – 3y)3

2.(x – 2) 3

3.(2x + 2a) 3

4.(5x – 3y) 3

5.(2a + b) 3

6.(2y – z) 3

7.(x – 5) 3

8.(2x + 7y) 3

9.(2ay2 – 4ay) 3

10.(c2 – d2) 3


AnswersAnswers

Answers

1. 8x2 – 36x2y + 54xy2 – 27y3

2. x2 – 6x2 + 12x - 83. 8x3 + 24ax2 + 24a2x + 8a3

4. 125x3 – 225x2y + 135xy2 – 27y3

5. 8a3 + 12a2b + 6ab2 – b3

6. 8y3 + 12y2z + 6yz2 – z3

7. x3 – 15x2 + 75x - 1258. 8x3 + 84x2y + 294xy2 + 343y3

9. 8a3y6 – 48a3y5 – 96a3y4 – 64a3y3

10. c6 – 3c4 d2 + 3c2d4 – d6

Questions Questions



___________________________ Objectives:


2.To know the relationship of squaring a binomials and cubing a binomials.

3.To be have more patient in squaring and cubing binomials.

Objectives:


2.To know the relationship of squaring a binomials and cubing a binomials.

3.To be have more patient in squaring and cubing binomials.

INSTRUCTION: Cube the following binomials. Show your complete solution in the box.

1.(3x + 4y) 3

2.(7x2+ y4) 3 3.(4f -8y)3 4.(4y3

+ 3y2) 3 5.(xy2

+ wz2) 3 6.(3w + 4z) 3

7.(y3- 8) 3

8.(9l + 8t) 3

9.(2o3 + 2x4) 3

10.(ax – 2xy) 3


AnswersAnswers

Answers

1. 27x3 + 108x2y + 144xy2 + 64y3

2. 343x6 + 147x4y4 – 21x2y8 + y2

3. 64f3 – 384f2y + 768fy2 – 512y3

4. 64y9 + 144y8 + 108y7 + 27y6

5. x3y6 + 3x2y4wz2 + 3xy2w2z4 + w3z6

6. 27w3 + 108w2z + 144wz2 + 64z3

7. y9 – 24y6 + 192y3 - 5128. 729l3 + 1944l2t + 1728lt2 + 512t3

9. 8o9 + 24o6x4 + 24o3x8 + 8x12

10. a3 x3 – 6a2x3y + 12ax3y2 – 8x3y

Questions Questions



___________________________ Objectives:

1.To recall how to solve the special products of binomial.

2.To have more practice in solving the special products of binomial.


Objectives:

1.To recall how to solve the special products of binomial.



INSTRUCTION: Solve the following binomial and get their special products. Show your complete solution and box your answer.

1.(a + 2)(a + 8)

2.(l + 6) (l + 9)

3.(e + 5) (e + 7)

4.(t + 2) (t + 6)

5.(h + 3) (h + 5)

6.(x + 4) (x + 2)

7.(m + 5) (m – 6)


AnswersAnswers

8. (j2 + 6) (j2 + 8)

9. (e3 + 2) (e3 – 4)

10. (r4 – 3) (r4 + 5)

11. (3x + 8)(7x + 9)

12. (2x + 4)(4x + 6)

13. (5x + 2)(3x + 4)

14. (6x + 3)(4x + 2)

15. (2x + 4)(8x + 5)


Answers

1. a2 + 109 + 162. l2 + 15l + 543. e2 + 12e + 354. t2 + 8t + 125. h2 + 8h + 156. x2 + 6x + 87. m2 – m – 30 8. j4 + 14j2 + 489. e6 – 2e3 – 8 10. r8 + 2r – 15 11. 21x2 + 83x + 7212. 8x2 + 28x + 2413. 15x2 + 26x + 814. 24x2 + 24x + 615. 16x2 + 42x + 20




___________________________Objectives:

1.To have a mastery in getting the special products of the binomials.

2.To be more efficient in using the FOIL method.


Objectives:

1.To have a mastery in getting the special products of the binomials.

2.To be more efficient in using the FOIL method.


INSTRUCTION: Encircle the product of the following equation and box the third term of each product. 1.(x - 20) (x + 3)2.(y + 1) (y – 2)3.(k + 30) (k + 5)4.(a – 4) (a + 6)5.(x – 9) (x + 3)6.(m + 8) (m + 5)7.(f +2) (f – 8)


AnswersAnswers

8. (w + 4) (w + 11)

9. (j + 5) (j – 3)

10. (x + 19) (x – 6)

11. (3x + 5) (2x + 35)

12. (3x2 + 3) (3x2 + 25)

13. (4a + 14) (6a + 39)

14. (5r + 7) (8r + 3)

15. (9q2 + 2)(2q2 – 5)


Answers

1. x2 – 17x - 602. y2 – y – 2 3. k2 + 35 k + 1504. a2 + 2a – 24 5. x2 – 6x – 27 6. m2 + 13m + 407. f2 – 6f - 168. w2 + 15w + 449. j2 + 2y – 15 10. x2 + 13x - 11411. 6x2 + 115x + 17512. 9x4 + 84x2 + 7513. 24a2 + 240a + 54614. 40r2 + 71r + 2115. 18q4 – 41q2 - 10

Questions 1 – 7 Questions 1 – 7 Questions 8 - 15Questions 8 - 15



___________________________Objectives:




Objectives:




INSTRUCTION: Solve the equation in the circle and box the product.

1.(i + 25) (i – 3)2.(i + 25) (i – 3)3.(o + 13) (o – 2)4.(x+ 5) (x – 1)5.(a + 8) (a + 9)6.(a + 9) (a – 11)7.(p + 5) (p + 4) 8.(s + 5) (s + 6)9.(c + 10) (c – 3)10.(q2 + 5) (q2 – 2)


AnswersAnswers

Answers

1. i2 + 22i - 752. i2 + 22i - 753. 02 + 11o - 264. x2 + 4x - 55. a2 + 17a + 726. a2 – 2a – 99 7. p2 + 9p + 208. s2 + 11s + 309. c2 + 7c - 3010. q4 + 3q2 - 10

Questions Questions

Post Test IIIName: __________________________Score:


___________________________

Objectives:

1.To recall all the ways in getting the special products of the polynomial.

2.To have more practice solving polynomials.


Objectives:

1.To recall all the ways in getting the special products of the polynomial.

2.To have more practice solving polynomials.



AA BB CC

INSTRUCTION: Solve the following polynomials and get their special products. Show your solution and box your final answer. A. Square the following monomials and binomials.

1.(er3) 2

2.(5y2) 2

3.(12d) 2

4.(7jy) 2

5.(vx) 2

6.(7k4x) 2

7.(2way2hz3z) 2

8.(12r5t6) 2

9.(26m3a) 2

10.(13kl2t6) 2 11.(u – 10)2

12.(2x7y + 3) 2

13.(5xa +2) 2

14.(f2 _ 2c) 2

15.(x + 13) 2

16.(16a2 + b) 2

17.(2p + 2q) 2

18.(2am +3z) 2

19.(9y2 + 5xy) 2

20.(27hx + 6og) 2


B. Cube the following binomials

1.(5ax – 23by)3

2.(2x – 6) 3

3.(2fx + 2h) 3

4.(5c – 4) 3

5.(7a +2k) 3

6.(8yk – z) 3

7.(2x2 – 3) 3

8.(5k + 8l) 3

9.(7ax2 – 2ay) 3

10.(3hx +7y) 3


C. Solve the following equations.

1.a2(f2 + a2y + 6)

2.m(6a2 – 9a – 10)

3.4x(2x3 + gx + 8)

4.3r(2rst + 20r2t + 3s)

5.mno(mn – m + o – 3)

6.kx (9k2 + kxy2 + k2y)

7.2ab (3cd2-7ab –5cd3)

8.x6(2x+ 3x – 5 )

9.2xz (14x3 + 4y + 12z)

10.x5(8x2 + 23x + 7)

11.12x2(5xy2 + 17x +x3)

12.(s + 3) (s – 7)

13.(m + 16) (m – 32)

14.(x + 2) (x – 5)

15.(t + 11) (t + 19)


16. (k + 5) (k – 18)

17. (q + 2) (q + 4)

18. (y + 3) (y + 7)

19. (u + 15) (u – 2)

20. (x2 + 2) (x2 – 4)

21. (w 3 + 5) (w3 + 8)

22. (3l + 7) (4l + 2)

23. (2x2 + 4) (3x2 + 6)

24. (2y + 15) (6y + 33)

25. (5t + 3) (4t + 8)

26. (3q2 + 1)(2q2 – 9)

27. (11v + 2) (5v + 1)

28. (2ua + 1) (8ua + 2)

29. (7b – 2)(3b – 6)

30. (24x – 1) (27x + 2)


Answers

1. e2r6

2. 25y4

3. 144d2

4. 49j2y2

5. y2x2

6. 49k8x

7. 4w29y4hz6z

8. 144r10t12

9. 676m6a

10. 169k2l4t12

11. u2 – 20u + 10012. 4x14y + 12x7y +913. 25x2a + 20xa + 414. f4 - 4cf2 + 4c2

15. x2 + 26x + 16916. 256a2 + 32a2b + b2

17. 4p2 + 8pq + 4q2

18. 4a2m + 12am z + 9z2

19. 81y4 + 90xy3 + 25x2y2

20. 729h2x + 324hxog + 36o2g

Questions AQuestions A

Answers

1. 12a3x2 – 175a2bx2y + 7 935ab2xy2 – 12 167b3y3

2. 8x3 – 72x2 + 216x - 216

3. 8f3x3 + 24f2hx2 + 24fh2x + 8h3

4. 125c3 – 300c2 + 240c - 64

5. 343a3 + 294a2k + 84ak2 + 8k3

6. 512y3k – 192y2kz – 24ykz2 – z3

7. 8x6 – 36x4 – 54x2 - 27

8. 125k3 – 600k2l + 960kl2 + 512l3

9. 343a3x6 – 294a3x4y + 84a3x2y2 – 8a3y3

10. 27h3x3 – 189h2x2y + 441hxy2 + 343y3

Questions BQuestions B

Answers

1. a2f2 – a4y + 6a2

2. 6a2m – 9am – 10m

3. 8x4 + 4ax2 + 32x

4. 6r2st + 60r3t + 9rs

5. m2n2o – m2no + mno2 – 3mno

6. 9k3 x + k2x2y2 + k3xy

7. 6abcd2 – 14a2b2 – 10abcd3

8. 5x7 – 5x6

9. 28x4z + 8xyz + 24xz2

10. 8z7 + 25x6 + 7x5

11. 60x3 y2 + 204x3 + 12x5

12. s2 – 4s - 21

13. m2 – 16m + 512

14. x2 – 3x - 10

15. t2 + 30t + 209

Questions C_1 - 15Questions C_1 - 15

Answers

16. k2 – 13k - 90

17. q2 + 6q + 8

18. y2 + 10y + 21

19. u2 + 13u - 30

20. x4 – 2x2 – 8

21. w6 + 13w3 + 40

22. 12l2 + 34l + 14

23. 6x4 + 24x2 + 24

24. 12y2 + 146y + 495

25. 20t2 + 52t + 24

26. 6q4 – 16q - 9

27. 55v2 + 21v + 2

28. 16u2a + 12ua + 2

29. 21b2 – 48b + 12

30. 648x2 + 21x - 2

Questions C_1 - 15Questions C_1 - 15

Pre Test IVName: __________________________ Score:_____________Date:_______________Year and Section: ________________ Teacher: _______________________________

Objectives:

1.To recall different types of factoring polynomial.

2.To get and write the factors of the polynomials.

3. To have patience in finding the factor of a polynomial.

4.To increase proficiency in factoring a polynomials.

Objectives:

1.To recall different types of factoring polynomial.

2.To get and write the factors of the polynomials.

3. To have patience in finding the factor of a polynomial.


TABLE OF CONTENTSTABLE OF CONTENTSTABLE OF CONTENTSTABLE OF CONTENTS


A , BA , B C , DC , D E , FE , F

G , HG , H

I , JI , J

K , LK , L M , NM , N OO

A. Instruction: Tell whether if the common factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor

__________1. The factor of 2x² - 6x + 8 is 2(x²– 3x + 4).

__________2. The factor of 5x + 30 is 5(x + 6).

__________3. The factor of 24x³ - 64y³ is 8(3x³ + 8y³).

__________4. The factor of 625x³ - 100y² is 25(25x³ + 5y²).

__________5. The factor of 2x³ + 4x² - 10x is 2(x³ + 2x² - 5x).

B. Instruction: Match the polynomial in column A to its proper and common factor in column B. Write the letter of your answer in the space provided before each number.

A B_____1. 3x + 9y a. 5 (x + 6)_____2. 2x³ + 4x² - 10x b. 2x (x² - 2x – 3)_____3. 6a³b + 3a²b² - 18ab³ c. 2x (x² + 2x – 5)_____4. 5x + 30 d. 3 (x + 3y)_____5. 2x³ - 4x² - 6x e. 3 (3a³b + a²b² - 6ab³)

PREVIOUSPREVIOUS NEXTNEXT ANSWERSANSWERS

C. Instruction: Factor the following algebraic expression. Get their common factor. Write your answer in the space provided.

1. 6c4 – 8c³ - 2c²2. 2b³ - 4b² - 8b + 103. 3y⁶ - 12y³ - 5y4. 3ax² - 6a²x + 9a³x5. 18x² - 24xy + 3y²

D. Instruction: Tell whether if the factor of the following polynomial is correct.Write A if the factor is correct and B if the factor is incorrect and write the correctfactor. _____1. The factor of m² - 144 is (m + 7) (m + 7)._____2. The factor of b²x² - y² is (b + y) (x – y)._____3. The factor of 25 - p² is (5 + p) (5 – p)._____4. The factor of 64x²y² - x² is (8xy + y) (8xy – x)._____5. The factor of c² - d⁴ is (c + d²) (c - d²).


E. Instruction: Tell whether if the factor by grouping of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of ax + ay + bx + by is (a + b) (x + y)._____2. The factor of 2x +8y – 3px -12py is (2 – 3p) (x + 4y)._____3. The factor of 3x – 3y + 4ay – 4ax is (3 – 4a) (x – y)._____4. The factor of x³ + 7x² + 2x ² 14 is (x² + 2) ( x + 7)._____5. The factor of 3x² + xy -12x -4y is (x – 4) (3x + y).

F. Instruction: Match the polynomials in column A to its proper factor of grouping in column B. Write your answer in the space provided before each number. A B_____1. 15x⁴ - 15x² + 5x² a. 2a³b² (a² + 4ab - 2b²)_____2. 2a⁵b² + 8a⁴b³ -4a³b⁴ b. (4x – 5) (x + 3)_____3. a³ -2a² + 5a – 10 c. 5x² (x² - 3x + 1)_____4. 3xy + 21x -2y – 14 d. (a – 2) (a² + 5)_____5. 5x² + 11x + 2 e. (x – 4y) (2x + 3y)


G. Instruction: Factor the following algebraic expressions by grouping. Write your answer in the space provided. 1. 27x³ + 108x² + 144x + 642. 4b² + 12bc + 9c² - 25d3. 36x² - 9y² + 24yz- 16z²4. ax² -4a + 3x² - 1236x² - 9y² + 24yz – 16z²

H. Instruction: Match polynomials in column A to its correct factoring which is the difference of two squares in column B. Write your answer in the space provided before each number.

A B_____1. x² - 9 a. (x⁴ + y⁴) (x² + y²) (x + y) (x – y)_____2. 4x² - 36y⁶ b. 4xy (2x + 3y) (2x - 3y)_____3. 49x⁴ - 36y⁴ c. (x + 3) (x – 3)_____4. x⁸ - y⁸ d. (7x² + 6y²) (7x² - 6y²)_____5. (t + 4)² - 9 e. (t + 7) (t + 1)


I. Instruction: Factor the difference of the two squares of the given polynomials. Write your answer in the space provided. 1. 81a² - 256b⁴2. 100 – 169z²3. 121 – 100x²y²4. 25m² - 36n²5. 64x²y⁴ - 1

J. Instruction: Find the missing term to make the expression a perfect trinomial square. 1. x + __________ + 92. a² + 8a + _______ 3. ______ + 2ab + b²4. 64x²y² + 80xyz + ________ 5. 25a² + _______ + 16b²


K. Instruction: Match polynomials in column A to its correct factor which is aperfect trinomial square in column B.

A B_____1. 4x² + 4x + 1 a. (2x + 3)²_____2. 25y² - 40y + 16 b. (2x + 1)²_____3. x² - 8x + 16 c. (x – 4)² _____4. a² + 14a + 49 d. (a + 7)²_____5. 4x² + 12x + 9 e. (5y – 4)²

L. Instruction: Factor the following polynomials by a perfect trinomial square.Write you answer in the space provided. 1. x² + 12x + 362. x² + 12xy + 9y²3. x² - 4x + 44. x² + 8x + 165. 36a² - 48a + 16


M. Instruction: Tell whether if the factor of the following equations is a factor ofgeneral quadratic trinomial. Write A if the factor is correct and B if the factor isincorrect and write the correct factor. _____1. The factor of 8p² + 24p + 18 is (2p + 3) (4p + 6)._____2. The factor of 15x² + 41x + 28 is (3 + 4) (5x + 7)._____3. The factor of 12b² + 17b – 5 is (2b + 1) ( 6b – 5)_____4. The factor of 24m² + 50mn – 9 is (4m + 3) (6m – 3)._____5. The factor of 6y² + 7y - 20 is (3y + 10) (2y – 2).

N. Instruction: Match the polynomials in column A to its correct factor which is in the general equation in column B.

A B_____1. (4x – 5) (x + 3) a. 3x² + 17x + 20_____2. (x + 5) (x + 5) b. x² + 10x + 25_____3. (p – 3) (p + 2) c. 2x² - 10 x + 12_____4. (2x – 6) (x – 2) d. p² - p – 6_____5. (x + 4) (3x + 5) e. 2x² - 10x + 12


O. Instruction: Factoring the sum and difference of cubes of the followingpolynomials. Write the letter of your answer in the space provided. 1. x³ - 82. 27x³ + 13. x³y⁶ - 644. 8x³ + 275. x³ + 1


A.

1. A2. A3. A4. B 25(25x³ - 5y²)5. A

Answers

B.

1. D2. C3. E4. A5. B

C.

1. 2c2(3c2 – 4c - )12. 2(b3 – 2b2 – 4b + 53. y(3y5 – 12y2 – 5)4. 3ax(x – 2a + 3a2)5. 3(6x2 – 8xy + y2)

D.

1.B (m + 12) (m – 12) 2. B (bx – y) (bx + y)3. A4. B (8xy – x) (8xy +x5. A

Questions AQuestions A Questions CQuestions CQuestions BQuestions B Questions DQuestions D

E.

1. A2. A3. B (3 + 4a) ( x – y)4. A5. A

F.

1. C2. A 3. D4. E5. B

G.

1. 2.3.4.5.

H.

1. C2. B3. D4. A 5. E

Questions HQuestions HQuestions GQuestions GQuestions FQuestions FQuestions EQuestions E

I.

1. (9a+16b2)(9a-16b2

2.(5+13z)(5 -13z)3. (11-10xy)(11+10xy)4. (5m–6n)(5m+6n)5. (8xy2–1) (8xy2 +1)

O.

1. (x-2) (x² - 2x + 4)2. (3x + 1) (9x² +3x + 1)3. (xy - 8) (x2y5 -8xy+ 8)4. (2x + 3) (4x3 +6x + 9)5. (x + 1) (x2 + x + 1)

N.

1. E2. B3. D4. C5. A

J.

1. 6x2. 163. a2

4. 255. 40ab

M.

1. A2. A3. B (4b - 1) ( 3b + 5)4. B (6m - 1) (4m + 9)5. B (3y - 4) (2y + 5).

K.

1. B2. E3. C4. D5. A

L.

1. (x+6)2

2.(x+3)2

3. (x – 2)2

4. (x+4)2

5. (6a – 4)2

Questions IQuestions I Questions JQuestions J Questions KQuestions K Questions LQuestions L

Questions OQuestions OQuestions MQuestions M Questions NQuestions N

Activity 37

Name: _________________________Score:_________Date:___________Year and Section: ________________ Teacher: ______________________

Objectives:

1.To recall how to factor a polynomial out of common factor.

2.To get and write the common factor.

3.To increased proficiency in factoring a polynomial out of common factor.

Objectives:



3.To increased proficiency in factoring a polynomial out of common factor.

Instruction: Tell whether if the common factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor.

_____1. The factor of 2x² - 6x + 8 is 2(x²– 3x + 4)._____2. The factor of 5x + 30 is 5(x + 6)._____3. The factor of 24x³ - 64y³ is 8(3x³ + 8y³)._____4. The factor of 625x³ - 100y² is 25(25x³ + 5y²)._____5. The factor of 2x³ + 4x² - 10x is 2(x³ + 2x² - 5x)._____6. The factor of 16x² - 24xy is 8(2x – 3y)._____7. The factor of 6a² - 9ab is 3(2a² - 3b)._____8. The factor of 12a²b – 18a³b is 6a(2b – 3ab)._____9. The factor of 9ay + 3a² - 6ay² is 3a(3ay + a² - 2ay²)._____10. The factor of 2n² - 6n + 4 is 2(n² - 3 + 2).


AnswersAnswers

Answers

1. A2. A3. B 8(3x3 – 8y3)4. B 25(25x3 – 4y2)5. A6. B 8x(2x – 3y)7.B 3a(2a – 3b)8. B 6ab(2a – 3a2)9. B 3a(3y + a – 2y2)10. B 2(n2 – 3n + 2)

QuestionsQuestions

Activity 38Name:_______________________Score:_____________Date:_____________Year and Section: _________________Teacher: _________________________

Objectives:

1.To identify the common factor of a polynomial.


3.To increase proficiency in factoring a polynomial out of common factor.

Objectives:

1.To identify the common factor of a polynomial.


3.To increase proficiency in factoring a polynomial out of common factor.

Instruction: Match the polynomial in column A to its proper and common factor in column B. Write the letter of your answer in the space provided before each number.

A B_____1. 3x + 9y a. 2(x² - 3x + 4)_____2. 2x³ + 4x² - 10x b. 25(25x³ - 5y²)_____3. 6a³b + 3a²b² - 18ab³ c. 2x(x² - 2x – 3)_____4. 5x + 30 d. 5(x + 6)_____5. 2x³ - 4x² - 6x e. 8 (3x² - 8y²)_____6. 625x³ - 100y² f. 2x(x² - 2x – 3)_____7. 18x³ -24x² + 3x g. 11a(1 + 2a)_____8. 2x² - 6x + 8 h. 3(x + 3y)_____9. 11a + 22a² i. 3x(6x² - 8x + 1)_____10. 24x³ - 64y² j. 3a (6a² + ab – 6b²) PreviousPrevious NextNextTABLE OF CONTEN

TSTABLE OF CONTENTS

AnswersAnswers

Answers

1. H2. F3. J4. D5. C6. B7. I8. A9. G10. E

QuestionsQuestions

Activity 39Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________Objectives:


2.To have patience in finding a common factor of a polynomial.

3.To show the solution in finding the common a factor of a polynomial.

Instruction: Factor the following algebraic expression. Get their common factor.Write your answer in the space provided.

1. 2ab + 8a²b²c² - 16a³b³c³2. 10a²y³ + 4ay3. 2c³ - 4c² - 6c 4. 11m + 22m²5. 12a³ - 24a² - 48a6. 6c4 – 8c³ - 2c²7. 2b³ - 4b² - 8b + 108. 3y⁶ - 12y³ - 5y9. 3ax² - 6a²x + 9a³x10. 18x² - 24xy + 3y²


AnswersAnswers

Answers

1. 2(ab + 4a2b2c2 – 8a3b3c3

2. 2ay(5ay2 + 2)3. 2c(c2 – 2c – 3)4. 11m(1 + 2m)5. 12a(a2 – 2a – 4)6. 2c(3c3 – 4c2 – c)7. 2(b3 - 2b2 – 4b + 5)8. 3y(y5 – 4y2 – 5)9. 3ax(x – 2a + 3a2)

10. 3(6x2 – 8xy + y2)

QuestionsQuestions

Activity 40Name: _______________________Score:_____________Date:__________Year and Section: _________________Teacher: ______________________

Objectives:

1.To recall how to factor a polynomial by grouping.

2.To find the factor of a polynomial by grouping.

3.To increase proficiency in factoring a polynomial by grouping.

Objectives:




Instruction: Tell whether if the factor by grouping of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of ax + ay + bx + by is (a + b) (x + y)._____2. The factor of 2x +8y – 3px -12py is (2 – 3p) (x + 4y)._____3. The factor of 3x – 3y + 4ay – 4ax is (3 – 4a) (x – y)._____4. The factor of x³ + 7x² + 2x ² 14 is (x² + 2) ( x + 7)._____5. The factor of 3x² + xy -12x -4y is (x – 4) (3x + y)._____6. The factor of 2a²x – 8b²x + a² - 4b²y is (2x + y)(a + 2b)(a + 2b)._____7. The factor of x² + 2xy + y² - z² is (x + y + z) (x + y + z)._____8. The factor of mx² - my² + nx² -ny² is (m + n) (x + y)._____9. The factor of x² - y² + 4yz – 4z² is (x + y – z) (x – y + z)._____10. The factor of 9a⁴b³ + 15a³b² - 3a²b is (3ab + 3ab) (5ab – 1).


AnswersAnswers

Answers

1. A2. A3. A4. A5. A6. B (2x + y)(a - 2b)(a + 2b)7. B (x + y + z) (x + y - z).8. B (m + n) (x + y) (x – y)9. A10. B (3a2b + 5ab) (3a2b – 1).

QuestionsQuestions

Activity 41

Name:_______________________Score:_____________Date:___________Year and Section: _________________Teacher: _______________________

Objectives:

1.To identify the factor of a polynomial by grouping.



Objectives:

1.To identify the factor of a polynomial by grouping.



Instruction: Match the polynomials in column A to its proper factor of grouping in column B. Write your answer in the space provided before each number.

A B_____1. 15x⁴ - 15x² + 5x² a. (x – 4y) (2x + 3y)_____2. 2a⁵b² + 8a⁴b³ -4a³b⁴ b. (5x + 1) (x + 2)_____3. a³ -2a² + 5a – 10 c. 5x² (x² - 3x + 1)_____4. 3xy + 21x -2y – 14 d. (3 + a) (x – 5)_____5. 5x² + 11x + 2 e. (a – 2) (a² + 5)_____6. 4x² + 7x – 15 f. (x + 4) (x -3)_____7. x³ - 3x + 4x – 12 g. (4x – 5) (x + 3)_____8. 2x² +3xy - 8xy – 12y² h. (y + 7) (3x – 2)_____9. 3x – 15 + ax – 5a i. (x + 4) (x – 6)_____10. x² - 6x + 4x – 24 j. 2a³b² (a² + 4ab - 2b²)


AnswersAnswers

Answers

1. C2. J3. E4. H5. B6. G7. F8. A9. D10. I

QuestionsQuestions

Activity 42Name: ________________________Score:_____________ Date: _________Year and Section: _________________Teacher: _______________________

Objectives:


2.To have patience in finding a factor of a polynomial by grouping.

3.To show the solution in finding the factor of a polynomial by grouping.

Objectives:


2.To have patience in finding a factor of a polynomial by grouping.

3.To show the solution in finding the factor of a polynomial by grouping.

Instruction: Factor the following algebraic expressions by grouping. Write your answer in the space provided. 1. 27x³ + 108x² + 144x + 642. 4b² + 12bc + 9c² - 25d3. 36x² - 9y² + 24yz- 16z²4. ax² -4a + 3x² - 125. 36x² - 9y² + 24yz – 16z²6. 16p² - t² + 2st - s²7. ac + 2bc – ad – 2bd8. 27m + 27 n – mn³ - n⁴9. 30mx + 18my – 10nx - 6ny10. 4a²m + 4a²n - b²m - b²n


AnswersAnswers

Activity 43Name: _______________________Score:_____________ Date:_______Year and Section: _________________Teacher: ____________________

Objectives::

1.To recall how to factor a polynomial of the difference of two squares.

2.To find the factor of difference of two squares.

3.To increase proficiency in factoring the difference of two squares.

Objectives::

1.To recall how to factor a polynomial of the difference of two squares.

2.To find the factor of difference of two squares.


Instruction: Tell whether if the factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of m² - 144 is (m + 7) (m + 7)._____2. The factor of b²x² - y² is (b + y) (x – y)._____3. The factor of 25 - p² is (5 + p) (5 – p)._____4. The factor of 64x²y² - x² is (8xy + y) (8xy – x)._____5. The factor of c² - d⁴ is (c + d²) (c - d²)._____6. The factor of a² b² - 36x² is (a² + 6x) (b² - 6x)._____7. The factor of x⁴y⁴ - 9 is (x⁴ + 3) (y⁴ -3)._____8. The factor of 49 – a⁶ is (7 + a³) (7 - a³)._____9. The factor of 64y² - 121 is (8y + 11) (8y – 11)._____10. The factor of 9x² - 16 is (3x + 4) (3x – 4).


AnswersAnswers

Answers

1. B (m + 7) (m - 7)2. B (bx + y) (xx – y)3. A 4. B (8xy + x) (8xy – x)5. A6. A7. A8. A9. A10. A

QuestionsQuestions

Activity 44Name: _______________________ Score:_____________Date: _________Year and Section: _________________Teacher: _______________________

Objectives:

1.To identify the factor of the difference of two squares.

2.To find the factor of the difference of two squares.


Objectives:

1.To identify the factor of the difference of two squares.

2.To find the factor of the difference of two squares.


Instruction: Match polynomials in column A to its correct factoring which is the difference of two squares in column B. Write your answer in the space provided before each number.

A B_____1. x² - 9 a. (x⁴ + y⁴) (x² + y²) (x + y) (x – y)_____2. 4x² - 36y⁶ b. 4xy (2x + 3y) (2x - 3y)_____3. 49x⁴ - 36y⁴ c. (x + 3) (x – 3)_____4. x⁸ - y⁸ d. (x³ + 2) (x³ - 2)_____5. (t + 4)² - 9 e. (6x + 1) (6x – 1)_____6. 16x³y – 36xy³ f. 2 (81x⁴ - 16y⁸)_____7. 12x³ - 27xy² g. (7x² + 6y²) (7x² - 6y²)_____8. 162x⁴ - 32y⁸ h. ( t + 7) (t + 1)_____9. x⁶ - 4 i. 3x (4x² - 9y²)_____10. 36x² - 1 j. 4x² (1 + 3y²) (1 - 3y²)


AnswersAnswers

Answers

1. C2. J3. G4. A5. H6. B7. I8. F9. D10. E

QuestionsQuestions

Activity 45Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________

Objectives:

1.To recall how to factor the difference of two squares.

2.To have patience in finding the factor of the difference of two squares.

3.To show the solution in finding the factor of the difference of two squares.

Objectives:

1.To recall how to factor the difference of two squares.

2.To have patience in finding the factor of the difference of two squares.

3.To show the solution in finding the factor of the difference of two squares.

Instruction: Factor the difference of the two squares of the given polynomials.Write your answer in the space provided. 1. 81a² - 256b⁴2. 100 – 169z²3. 121 – 100x²y²4. 25m² - 36n²5. 64x²y⁴ - 16. 9x² - 25a²7. x⁴y⁴ - 648. 4x² - 169. m⁴n²p² - 121a²10. 49m⁴x²y² - 16a²


AnswersAnswers

Answers

1. (9a + 16b2) (9a – 16b2)2. (10 + 13z) (10 – 13z)3. (11 + 10xy) (11 – 10xy)4. (5m + 6n) (5m – 6n)5. (8xy + 1) (8xy – 1)6. (3x + 5a) (3x – 5a)7. (x2y2 + 8) (x2y2 – 8)8. (2x + 4) (2x – 4)9. (mnp + 11a) (mnp – 11a)10. (7m2xy + 4a) (7m2xy – 4a)

QuestionsQuestions


1.To recall how to factor a perfect trinomial square.

2.To get and write the factor of a perfect trinomial.

3.To increase proficiency in factoring a perfect trinomial square.

Objectives:


2.To get and write the factor of a perfect trinomial.


Instruction: Find the missing term to make the expression a perfect trinomial square. 1. x + _____ + 92. a² + 8a + _____ 3. _____ + 2ab + b²4. 64x²y² + 80xyz + _____ 5. 25a² + _____ + 16b²6. 4m² + _____ + 25n²7. x² + _____ + 4 8. _____ + 6a + 99. 25a² + 40ab + _____ 10. _____+ 80xyz + 25z²


AnswersAnswers

Answers

1. 6x2. 163. a2

4. 25z2

5. 40ab6. 20mn7. 4x8. a2

9. 16b2

10. 64x2y2

QuestionsQuestions


Objectives:

1.To identify the factor of a perfect trinomial square.

2.To get the factor of a perfect trinomial square.


Instruction: Match polynomials in column A to its correct factor in column B. which is a perfect trinomial square

A B_____1. 4x² + 4x + 1 a. (2x + 3)²_____2. 25y² - 40y + 16 b. (2x + 1)²_____3. x² - 8x + 16 c. (x + 3)²_____4. a² + 14a + 49 d. (2x – 5)²_____5. 4x² + 12x + 9 e. (5y – 4)²_____6. x² + 2x + 1 f. (x + 9)²_____7. x² + 6x + 9 g. (a + 7)²_____8. 4x² -20x + 25 h. (x – 10)²_____9. x² + 18x + 81 i. (x + 1)²_____10. x² - 20x + 100 j. (x – 4)²


AnswersAnswers

Answers

1. B2. E3. J4. G5. A6. I7. C8. D9. F10. H

QuestionsQuestions


Objectives:


2.To have patience in factoring a perfect trinomial square.

3.To show the solution in factoring a perfect trinomial square.

Instruction: Factor the following polynomials by a perfect trinomial square.Write you answer in the space provided. 1. x² + 12x + 362. x² + 12xy + 9y²3. x² - 4x + 44. x² + 8x + 165. 36a² - 48a + 166. 49b² - 56b³xy² + 16x²y⁴7. 4x² - 12xy + 9y²8. 3x³y + 24x²y² + 48xy³9. x² + 6mx + 5m²10. x² + 4x – 4


AnswersAnswers

Answers

1. (x+6)2

2. (x+3y)2

3. (x-2)2

4. (x+4)2

5. (6a-4)2

6. (7b – 4xy)2

7. (2x + 3y)2

8. (3x2y+24xy2) (x + 2)9. (x + m) (x + 5m)10. (x + 2) (x – 2)

QuestionsQuestions


1.To recall how to factor a general quadratic trinomial.

2.To get the factor of general quadratic trinomial.

3.To increase proficiency in factoring a general quadratic trinomial.

Instruction: Tell whether if the factor of the following equations is a factor of general quadratic trinomial. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of 8p² + 24p + 18 is (2p + 3) (4p + 6)._____2. The factor of 15x² + 41x + 28 is (3 + 4) (5x + 7)._____3. The factor of 12b² + 17b – 5 is (2b + 1) ( 6b – 5)_____4. The factor of 24m² + 50mn – 9 is (4m + 3) (6m – 3)._____5. The factor of 6y² + 7y - 20 is (3y + 10) (2y – 2)._____6. The factor of 20a² + 21a + 4 is (5a + 4) (4a + 1)._____7. The factor of 12y² - 52y + 35 is (2y – 7) (6y – 5)._____8. The factor of 6m² - 7m – 24 is (3m – 8) (2m + 3)._____9. The factor of 32m² ⁸ 28m – 15 is (4m + 5) (8m – 3)._____10. The factor of 30b² - bd - 42d² is (6b + 7d) (5b – 6d).


AnswersAnswers

Answers

1. A2. A3. B (4b - 1) (3b + 5)4. B (6m - 1) (4m + 9)5. B (3y - 4) (2y + 5)6. A7. A8. A9. A10. A

QuestionsQuestions


Objectives:

1.To identify the factor of general quadratic trinomial.



Objectives:

1.To identify the factor of general quadratic trinomial.



Instruction: Match the polynomials in column A to its correct factor which is in the general equation in column B.

A B_____1. (4x – 5) (x + 3) a. 5x² + 11x + 2_____2. (x + 5) (x + 5) b. x² + 5x + 6_____3. (p – 3) (p + 2) c. y² - 5y + 4_____4. (2x – 6) (x – 2) d. p² - p – 6_____5. (x + 4) (3x + 5) e. x² + 10x + 25_____6. (5x + 1) (5x + 2) f. 5x² + 5x – 10_____7. (x + 2) (5x – 5) g. 4x² + 7x – 15_____8. (y – 1) (y – 4) h. x² - 12x + 36_____9. (x – 6) (x – 6) i. 2x² - 10x – 12_____10. (x + 3) (x + 2) j. 3x² + 17x + 20 PreviousPrevious NextNextTABLE OF CONTEN

TSTABLE OF CONTENTS

AnswersAnswers

Answers

1. G2. E3. D4. I5. J6. A7. F8. C9. H10. B

QuestionsQuestions


Objectives:


2.To have patience in factoring a general quadratic trinomial.

3.To show the solution in factoring a general quadratic trinomial.

Objectives:


2.To have patience in factoring a general quadratic trinomial.

3.To show the solution in factoring a general quadratic trinomial.

Instruction: Factor the following polynomials by general quadratic equation. 1. 16a² -16a - 272. 2b² - 3b – 143. 15p² -17p – 44. 5t² - 33t – 565. 80m² + 66m – 276. 56x² - 33x – 1087. 44d² - 47d – 108. 28 + 71n + 18n²9. 6 – 23x + 20x²10. 28 – 43y – 45y²


AnswersAnswers

Answers

1. (4a + 3) (4a – 9)2. (2b – 7) (b + 2)3. (3p – 4) (5p + 1)4. (t – 8) (5t + 7)5. (8m + 9) (10m – 3)6. (8x + 9) (7x – 12)7. (4d – 5) (11d – 2)8. (7 + 2n) (4 + 9n)9. (3 – 4x) (2 – 5x)10. (4 – 9y) ( 7 + 5y)

QuestionsQuestions


Objectives:

1.To recall how to factor the sum and difference of two cubes.

2.To get the factor of the sum and difference of two cubes.

3.To increase proficiency in factoring the sum and difference of two cubes.

Objectives:




Instruction: tell whether if the factor of the following expression is correct. Write A if the factor is correct and B if the factor is incorrect. _____1. The factor of 8 - t³ is (t – 2) (t² + 2t + 4)._____2. The factor of 64 – 8b³ is (2b – 8) (4b² + 16b + 8)._____3. The factor of m³ + 1 is (m + 1) (m² - m + 1)._____4. The factor of d³ + 27 is (d + 3) (d² - 3d + 9)._____5. The factor of 8a³ - 8 is (2a – 2) (4a² + 4a + 4)._____6. The factor of x³ + 125 is (x + 5) (x² - 5x + 25)._____7. The factor of 64p³ - 27 is (8p + 3) (8p² - 24p + 9)._____8. The factor of 8y³ + 1 is (2y + 2) (4y² - 4y + 1)._____9. The factor of a³ + 64 is (a + 4) (a² - 4a + 16)._____10. The factor of 8 - b³ is (2- b) (2² + 2b + 2).


AnswersAnswers

Answers

1. B2. B3. A4. A5. A6. A7. B8. B9. A10. B

QuestionsQuestions


Objectives:

1.To identify the factor of the sum and difference of two cubes.



Objectives:

1.To identify the factor of the sum and difference of two cubes.



Instruction: Match the polynomials column A to its correct factor which is the sum and difference of two cubes in column B.

A B_____1. x³ + 8 a. (4a + 3y) (16a² - 12ay + 9y²)_____2. 12b³ - 1 b. (2x + 3) (4x² - 6x + 9)_____3. 64a² + 27y³ c. (x – 3y) (x² + 3xy + 9y²)_____4. 27x³ - 64y³ d. (x + 2) (x² - 2x + 4)_____5. x³ - 27 e. (x – 3) (x² + 3x + 9)_____6. 8a³ + 125 f. (x – 3) (x² - 3x – 9)_____7. x³ - 9 g. (3x – 8y) (9x² + 24 + 8y²)_____8. 8x³ + 27 h. (4a + 5) (2a² - 20 + 25)_____9. x³ - 1 i. (x – 1) (x² - x + 1)_____10. x³ - 27y³ j. (5b – 1) (25b² + 5b + 1)


AnswersAnswers

Answers

1. D2. J 3. A4. G5. E6. H7. F8. B9. I10. C

QuestionsQuestions

Activity 54Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________ Objectives:


2.To have patience in factoring the sum and difference of two cubes.

3.To show solution in factoring the sum and difference of two cubes.

Instruction: Factoring the sum and difference of cubes of the following polynomials. Write the letter of your answer in the space provided. 1. x³ - 82. 27x³ + 13. x³y⁶ - 644. 8x³ + 275. x³ + 16. x³ + 87. (x + 1)³8. (3x + y)³9. (x + 2y)³10. (2x – 1)³


AnswersAnswers

Answers

1. (x-2) (x² - 2x + 4)2. (3x + 1) (9x² +3x + 1)3. (xy - 8) (x2y5 -8xy+ 8)4. (2x + 3) (4x3 +6x + 9)5. (x + 1) (x2 + x + 1)6. (x+2) (x² + 2x + 4)7. (x + 1) (x2 + x + 1)8. (3x + y) (3x2 + 3x + 1)9. (x + y) (x2 + 2x + 2)10. (2x – 1) (4x2 – 2x + 1)

QuestionsQuestions

Post Test IVName: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________

Objectives:

1.To recall different types of factoring of polynomial;

2.To get and write the factors of the polynomials;

3.To have patience in finding the factor of a polynomial; and


Objectives:

1.To recall different types of factoring of polynomial;

2.To get and write the factors of the polynomials;

3.To have patience in finding the factor of a polynomial; and



Instructions: Get the factor of the given polynomials. Show your solutions. Encircle your final answer 1. 2ab + 8a²b²c² - 16a³b³c³ 2. 10a²y³ + 4ay

3. 2c³ - 4c² - 6c 4. 11m + 22m² 5. 12a³ - 24a² - 48a 6. 6c4 – 8c³ - 2c² 7. 2b³ - 4b² - 8b + 10 8. 3y⁶ - 12y³ - 5y

9. 3ax² - 6a²x + 9a³x 10. 18x² - 24xy + 3y²


11. 27x³ + 108x² + 144x + 64 12. 4b² + 12bc + 9c² - 25d 13. 36x² - 9y² + 24yz- 16z² 14. ax² -4a + 3x² - 12

15. 36x² - 9y² + 24yz – 16z²

16. 16p² - t² + 2st - s² 17. ac + 2bc – ad – 2bd 18. 27m + 27 n – mn³ - n⁴ 19. 30mx + 18my – 10nx - 6ny

20. 4a²m + 4a²n - b²m - b²n


21. 81a² - 256b⁴ 22. 100 – 169z² 23. 121 – 100x²y² 24. 25m² - 36n²

25. 64x²y⁴ - 1

26. 9x² - 25a² 27. x⁴y⁴ - 64 28. 4x² - 16 29. m⁴n²p² - 121a²

30. 49m⁴x²y² - 16a²


31. x² + 12x + 36 32. x² + 12xy + 9y² 33. x² - 4x + 4 34. x² + 8x + 16 35. 36a² - 48a + 16 36. 49b² - 56b³xy² + 16x²y⁴ 37. 4x² - 12xy + 9y²

38. 3x³y + 24x²y² + 48xy³ 39. x² + 6mx + 5m² 40. x² + 4x – 4


41. 16a² -16a – 27 42. 2b² - 3b – 14 43. 15p² -17p – 4 44. 5t² - 33t – 56 45. 80m² + 66m – 27 46. 56x² - 33x – 108 47. 44d² - 47d – 10 48. 28 + 71n + 18n² 49. 6 – 23x + 20x²


50. 28 – 43y – 45y² 51. x³ - 8 52. 27x³ + 1 53. x³y⁶ - 64 54. 8x³ + 27 55. x³ + 1 56. x³ + 8 57. (x + 1)³ + 8 58. (3x + y)³ (3x – y)³ 59. (x + 2y)³ (x – 2y)³ 60. (2x – 1)³ - 8


Answers

QuestionsQuestions

11.12.13.14.15.16.17.18.19.20.

QuestionsQuestions QuestionsQuestions

1. 2(ab + 4a2b2c2 – 8a3b3c3

2. 2ay(5ay2 + 2)3. 2c(c2 – 2c – 3)4. 11m(1 + 2m)5. 12a(a2 – 2a – 4)6. 2c(3c3 – 4c2 – c)7. 2(b3 - 2b2 – 4b + 5)8. 3y(y5 – 4y2 – 5)9. 3ax(x – 2a + 3a2)

10. 3(6x2 – 8xy + y2)

21. (9a + 16b2) (9a – 16b2)22. (10 + 13z) (10 – 13z)23. (11 + 10xy) (11 – 10xy)24. (5m + 6n) (5m – 6n)25. (8xy + 1) (8xy – 1)26. (3x + 5a) (3x – 5a)27. (x2y2 + 8) (x2y2 – 8)28. (2x + 4) (2x – 4)29. (mnp + 11a) (mnp – 11a)30. (7m2xy + 4a) (7m2xy – 4a)

Answers

QuestionsQuestions QuestionsQuestions QuestionsQuestions

31. (x+6)2

32. (x+3y)2

33. (x-2)2

34. (x+4)2

35. (6a-4)2

36. (7b – 4xy)2

37. (2x + 3y)2

38. (3x2y+24xy2) (x + 2)39. (x + m) (x + 5m)310. (x + 2) (x – 2)

41. (4a + 3) (4a – 9)42. (2b – 7) (b + 2)43. (3p – 4) (5p + 1)44. (t – 8) (5t + 7)45. (8m + 9) (10m – 3)46. (8x + 9) (7x – 12)47. (4d – 5) (11d – 2)48. (7 + 2n) (4 + 9n)49. (3 – 4x) (2 – 5x)50. (4 – 9y) ( 7 + 5y)

51. (x-2) (x² - 2x + 4)52. (3x + 1) (9x² +3x + 1)53. (xy - 8) (x2y5 -8xy+ 8)54. (2x + 3) (4x3 +6x + 9)55. (x + 1) (x2 + x + 1)56. (x+2) (x² + 2x + 4)57. (x + 1) (x2 + x + 1)58. (3x + y) (3x2 + 3x + 1)59. (x + y) (x2 + 2x + 2)60. (2x – 1) (4x2 – 2x + 1)

BIBLIOGRAPHY

BOOKS

Baquial, Rene Isidro C. (1994). Algebraic Expression, Philippines: Rex Printing Company, Inc. Biscocho, Ma. Inocencia D. (1990). Polynomials, Philippines: Katha Publishing Co. Inc. Capitulo, Florante M. (1989). Factoring Polynomials, Philippines: National Book Store, Inc. Cariño, Isidro P. (1977). Simplifying Polynomials, Philippines: JMC Press, Inc. Petilos, Gabino P. (2004). Algebraic Expressions, Philippines: Trinitas Publishing Inc. Santos, E.Z. Doval, (1977). Factoring Polynomials, Philippines: Era Philippines Incorporated Spark, Fred W. (1990). Simplifying Polynomials, Philippines: McGraw-Hill Publishing Company

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APRYL JOY BANILA MERABIL is a daughter of Ms. Rowena S. Banila and Mr. Jose Gerry B. Merabil. She lives in Brgy. Macasipac Santa Maria, Laguna. She was born on January 25, 1992.

She finished her elementary level in Bagumbayan Elementary School Santa Maria, Laguna as a Valedictorian on the year 2004. She graduated her secondary level in Liceo De Pakil Pakil, Laguna on the year 2007. She finished her Bachelor of Secondary Education major in Mathematics from Laguna State Polytechnic University in Laguna.

APRYL JOY BANILA MERABIL is a daughter of Ms. Rowena S. Banila and Mr. Jose Gerry B. Merabil. She lives in Brgy. Macasipac Santa Maria, Laguna. She was born on January 25, 1992.

She finished her elementary level in Bagumbayan Elementary School Santa Maria, Laguna as a Valedictorian on the year 2004. She graduated her secondary level in Liceo De Pakil Pakil, Laguna on the year 2007. She finished her Bachelor of Secondary Education major in Mathematics from Laguna State Polytechnic University in Laguna.

EDLYN CATAPAT ORTIZ is a daughter of Ms. Connie O. Catapat and Mr. Ernesto C. Ortiz. She lives in Brgy. Talangka Santa Maria, Laguna. She was born on May 3, 1988.

She finished her elementary level in Bagong Pook Elementary School Santa Maria, Laguna on the year 2000. She graduated her secondary level in Santa Maria National High School Santa Maria, Laguna on the year 2004. She finished her Bachelor of Secondary Education major in Mathematics from Laguna State Polytechnic University in Laguna.

EDLYN CATAPAT ORTIZ is a daughter of Ms. Connie O. Catapat and Mr. Ernesto C. Ortiz. She lives in Brgy. Talangka Santa Maria, Laguna. She was born on May 3, 1988.

She finished her elementary level in Bagong Pook Elementary School Santa Maria, Laguna on the year 2000. She graduated her secondary level in Santa Maria National High School Santa Maria, Laguna on the year 2004. She finished her Bachelor of Secondary Education major in Mathematics from Laguna State Polytechnic University in Laguna.

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