PAP Pre-Calculus Assignment Sheet Unit 8 – Polynomial Functions

January 7-January 25

Date Lesson Assignment Monday Jan. 7

Staff Development-Student Holiday

Tuesday Jan. 8 Day 1

2.1 Obj: Students will write Quadratic Functions and sketch graphs. Procedures: 1) Work examples 2) Calendars for stamps

Homework: Pg. 134: 1-8, 15, 17, 19, 26, 28, 39, 47, 58, 63, 76, 85, 88

Wednesday Jan. 9 Day 2

2.2 Obj: Students will use sketch polynomial graphs. Procedures: 1) Discuss homework. 2) Work examples

Homework: Precal (GTH ) - Worksheet 2.2.doc

Thursday Jan. 10 Day 3

2.2 Obj: Students will find the zeros of polynomial functions and use them to sketch their graphs. Procedures: 1) Discuss homework. 2) Work examples

Homework: P. 149: 48-56 even, 71-80 all, 91

Friday Jan. 11 Day 4

2.3 Obj: Students will use long division and synthetic division to divide polynomials. (Remainder Theorem and Factor Theorem) Procedures: 1) Quiz over Polynomials (2.1-2.2). 2) Discuss homework 3) Work examples

Homework: Pg. 159: 7-8, 13-16, 21-35 odd, 69, 72, 79, 83

Monday January 14 Day 5

2.5 Obj: Students will use the Rational Root Theorem to find the real and imaginary roots Procedures: 1) Discuss homework. 2) Work examples

Homework: Precal (GTH ) - Worksheet 2.5.doc

Tuesday Jan. 15 Day 6

2.5 Obj: Students will use the Descartes Rule of Signs. Procedures: 1) Discuss homework. 2) Work examples

Homework: Precal (GTH ) - Worksheet 2.5 (Descartes).doc

Wednesday Jan. 16 Day 7

2.5 Obj: Students will use the Intermediate value theorem to approximate irrational roots Procedures: 1) Discuss homework. 2) Work examples

Homework: Precal (GTH ) - Worksheet 2.5(Approx. Zeros).doc

Thursday Jan. 17 Day 8

2.3 Obj: Students will write equations of polynomial given the graphs Procedures: 1) Discuss homework. 2) Work examples

Homework: WS 2.2-2.5.pdf On part III of Worksheet +6 was cut off the page

Friday Jan. 18 Day 9

2.3 & 2.5 Obj: Students will analyze and sketch graphs of polynomial functions. Procedures: 1) Discuss homework. 2) Quiz 2.3 & 2.5

Homework: WS 2.5-2.6.pdf

Monday Jan 21

Student Holiday

Tuesday Jan. 22 Day 10

2.7 Obj: Students will solve polynomial inequalities. Procedures: 1) Discuss homework 2) Work examples 2.7

Homework: Precal (GTH ) - Worksheet 2.7.doc

Wednesday Jan. 23 Day 11

2.7 Obj: Students will solve polynomial inequalities. Procedures: 1) Discuss homework 2) Quizlet time

Homework: Study for test, Finish any homework that you haven’t done so far.

Thursday Jan. 24 Day 12

2.1-2.5, 2.7 Obj: Students will review polynomial functions for test. Procedures: 1) Discuss homework. 2) Go over old quizzes

Homework: Study for test

Friday Jan. 25

Test 2.1-2.5, 2.7

Name_________________Per____ Graphing polynomials ( ) ( )( )322 1 1f x x x x= − − +

a) Roots:_____________ b) Y-int:_____________ c) Type:_____________

( ) ( )( ) ( )27 2 3 5f x x x x= − − +

a) Roots:_____________ b) Y-int:_____________ c) Type:_____________

( ) ( ) ( )( )2 22 3 2 3f x x x x= + − −

a) Roots:_____________ b) Y-int:_____________ c) Type:_____________

( ) ( ) ( )32 1f x x x x= + −

a) Roots:_____________ b) Y-int:_____________ c) Type:_____________

Worksheet 2.5 Rational Root Theorem Name_______________________________ Period_______

1. Determine the possible rational zeros of the polynomial. Show how you determine these possible roots/zeros. ( ) 4 3 2P x 3x 2x 7x 21= − + −

List all possible zeros: 2. Determine the following for the given polynomial: ( ) 3 2P x x x 5x 5= − − +

a) possible rational zeros:

b) rational zeros:

c) all zeros:

d) linear factors:

3. Determine the possible rational zeros the polynomial: ( ) 4 3P x 3x 2x 7x 24= − + − List all possible zeros: 4. Determine the following for the given polynomial: ( ) 3 2P x x 2x 7x 14= − − +

a) possible rational zeros:

b) rational zeros:

c) all zeros:

d) linear factors:

Find (a ) all of the zeros then (b) write as products of linear factors and sketch graph.

5. synthetic division possible zeros:

zeros: __________________________ linear factors: __________________________ 6. possible zeros:

zeros: __________________________ linear factors: __________________________ 7. possible zeros:

zeros: __________________________ linear factors: __________________________ 8. possible zeros:

zeros: __________________________ linear factors: __________________________ 9. possible zeros:

zeros: __________________________ linear factors: __________________________

3 2( ) 2 22 24f x x x x= − − −

3 2( ) 5 12 29 12g x x x x= + − +

3 2( ) 2 3 17 12g x x x x= + − +

3 2( ) 2 5 14 8f x x x x= − − +

3 2( ) 4 9 49 30g x x x x= + − +

Name ___________________________________________ Honors/PAP Precal Period_______ Descartes Rule Express as a product of linear factors. 1. f x x x x( ) = − − +3 23 10 24 ___________________________________

2. g x x x x( ) = − − +2 5 63 2 ___________________________________ Use Descartes’ Rule to determine the possible number of positive and negative real zeros of each polynomial. 3. g x x x( ) = − +2 5 74 2 4. g x x x x x( ) = − + − +7 13 9 5 45 4 3 2 5. 3 2( ) 25 25 26 2g x x x x= − − + Determine the possible rational zeros. 6. 3 2( ) 25 25 26 2g x x x x= − − + ____________________________________ 7. 3 2( ) 6 11 3 2f x x x x= − + + − ____________________________________ Determine the least integral upper bound and the greatest integral lower bound for the zeros of the polynomials. 8. g x x x x( ) = − + +24 74 21 543 2 UB:___________

LB:___________ 9. f x x x x x x( ) = + − − + +5 4 3 25 3 29 2 23 UB:____________

LB:_____________

pos neg im

pos neg im

pos neg im

10. 3 2( ) 4 14 10 3f x x x x= + + − UB:_____________

LB:_____________ 11. 3 2( ) 6 4 9 6f x x x x= + + + UB:______________

LB:_______________

Name _____________________________________________ Honors/PAP Precal Period_______ Approximating Zeros Determine the possible rational roots. 1. 3 2( ) 3 3 10 24f x x x x= − − + ___________________________________ Determine all of the zeros of each function. 2. 3 2( ) 2 12 9f x x x x= + − + ___________________________________ Determine a polynomial of lowest degree with rational coefficients that has the following zeros. Write in expanded form (mult out). 4. 3 2i− + and 5 ___________________________________ Determine the possible number of positive real, negative real, and imaginary zeros of each polynomial. 5. 4 3 2( ) 2 6 5 7g x x x x= − + + pos __________ neg _______imag _______ Determine the least integral upper bound and the greatest integral lower bound for the zeros of the polynomials. 6. 3 2( ) 12 44 23 105g x x x x= + − − UB_______LB_________ Graph the functions. 7 2( ) ( 3)( 1)( 5 6)f x x x x x= + + − − 8. 2( ) ( )( 5)f x x x x= − + − zeros ___________ zeros ____________ y-intercept ______ y-intercept ______

9) Given the following graph, find the equation that fits it best. Equation________________________ 10. 3 2( ) 4 2 5= − − +f x x x x Possible Rational Roots: ________________________ Roots (Exact values for all roots) _______________________ Graph Here

Approximating Irrational roots (Some will have roots that you can find exactly) Sketch each of these functions. Do a PNI Chart to help you sketch the graphs. 11) f(x) = x3 – x2 + 2x + 24 12) 5 3 2( ) 1= + − −f x x x x

13) 4 3 2( ) 3 5 2= + − − −f x x x x x 14) 3 2( ) 4 2 5= + + +f x x x x

15) 4 2( ) 2 3 6 5= + + −f x x x x

16) Is x + 1 or x - 1 factors of x100 – x50 + x27 + 1 ? Show why or why not.

pos neg im

pos neg im

pos neg im

pos neg im

pos neg im

pos neg im

Name_______________________________________ Period_______ PAP PreCalculus WS 2.5-2.6

1. Find k such that x – i is a factor of 4 2x kx 9+ −

II. Descartes’ Rule Make a p-n-i chart for each polynomial:

2. 5 3 23x x x 1− + − 3. 5 3x 11x 3x 5− − +

III. Given the polynomial ( ) 3P x x 15x 22= − −

4. List all the possible roots: 5. Complete a p-n-i chart

6. Find the roots and y-intercept and sketch the graph. If there are irrational roots, give decimal approximations for them. How many decimal places? 3

7. Find the quotient and remainder: ( ) ( )4 3x 6x 11x 5 x 4− + − ÷ +

IV. Find P(x) by any method:

8. Given: ( ) 51 30P x x 2x 1= − + , find P(-1) 9. Given: ( ) 4 2 1P x 4x 6x 10x 3, find P

2 = − − + −

10. If P(x) is divided by 3x – 4, the quotient is 2x x 2 and the remainder is 7. Find P(x)− +

11. Given that x = -2 is a root of 3 22x 2x x 10, find the other roots.+ + +

12. Given that x = 1 is a double root of 4 3 2x 2x 4x 6x 3, find the other roots.− + − +

PRECALCULUS GT/HONORS WORKSHEET ON 2.7 Solve each of the following and write your answer in interval notation. Show work on your own paper. There is not enough room on here to do the problems properly. 1. 2 7 10 0x x+ + ≥ 2. 22 4 5 0x x− − < 3. 2 1x x+ ≤ − 4. ( )( )( )1 3 3 1 0x x x+ − − ≥ 5. ( ) ( )( )2 32 4 5 0x x x− + − < 6. ( )( )( )2 3 4 3 5 0x x x x+ − − > 7. 325 4 0x x− ≤ 8. 3 23 24 48x x x+ < − 9. 4 2 12x x+ ≥ 10. 5 35 4x x x− > − 11. 3 24 4 0x x x− + < 12. 3 211 18x x x− ≥ − 13. 3 23 0x x− < 14. 4 225 0x x− ≥ 15. 3 23 84 28x x x− + ≤ 16. 3 25 6 10 12x x x+ > + 17. 3 25 2 10 0x x x+ − − < 18. 5 4 16 16 0x x x+ − − ≤