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Name Date Period Workbook Activity
Chapter 1, Lesson 11
Writing Equations
One-half of a number plus 3 is 13.
�12
�x � 3 � 13
Directions Write an equation for each statement. Let x be the number.
1. 6 times a number is 18. ___________________________
2. One-fifth of a number is 25. ___________________________
3. 8 plus some number is 22. ___________________________
4. Two-thirds of a number is 12. ___________________________
5. 4 times a number plus 4 is twice the number. ___________________________
6. A number plus one-fourth of the number is 150. ___________________________
7. 3 times a number subtracted from 45 is 30. ___________________________
8. 14 less than one-half of a number is 2 more than the number. ___________________________
Directions Circle the equation that solves the problem.
9. Sandra rode her bike 54 miles in one day. She rode 6 times thenumber of miles Caleb rode his bike. How many miles did Caleb ridehis bike? Let b represent the number of miles Caleb rode his bike.
A b � 54 � 6
B 54b � 6
C 6b � 54
10. Jordan went to Europe for vacation. He spent �23� of his time in Spain.If he was in Spain for 14 days, how long was he in Europe? Let v represent the number of days he was in Europe.
A �23�v � 14
B �23�(14) � v
C v � 14 � �23�
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
Name Date Period Workbook Activity
Chapter 1, Lesson 22
Axioms of Equality (Rules for Equations)
Directions Draw a line to match the axiom of equality on the left withthe statement on the right.
1. Reflexive Law
2. Symmetric Law
3. Transitive Law
4. Substitution Principle
If 3x � 15 and �12�y � 15, then 3x � �12
�y.
This statement illustrates the transitive law.
Directions Write the axiom of equality that is illustrated.
5. 14 � 2x and 2x � 14 ___________________________
6. 23y � 6 � 23y � 6 ___________________________
7. x � y and 4x � 17; 4y � 17 ___________________________
8. If 9m � 12 and n � 12, then 9m � n ___________________________
9. x � y and �13�y � 18; then �13
�x � 18 ___________________________
10. x � 8 � 12 and 12 � x � 8 ___________________________
11. 18 � �23�x � 15 and x � 3y; then 18 � �23
�(3y) � 15 ___________________________
Directions Complete each statement to illustrate the axiom ofequality given.
12. Substitution Principle: If a � b and b � 2 � 6, then a � ______ � 6
13. Reflexive Law: 8y � 3 � ______ � 3
14. Symmetric Law: If 3x � 7 � 15, then 15 � ______
15. Transitive Law: If 5x � 3 � 7 and 4x � 7, then 5x � 3 � ______
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
A If a � b, then b � a.
B Things that are equal to the same thing areequal to each other.
C Equals may be substituted for equals. If a � b,then b can be substituted for a in anymathematical statement without changing itstruth or falsehood.
D Anything is equal to itself.
EXAMPLE
Name Date Period Workbook Activity
Chapter 1, Lesson 33
Solutions by Addition or Subtraction
Write the missing step in solving the equation x � 1 � 3.
x � 1 � 3 x � 1 � 3
? � ? �1 � �1
x � 0 � 2 x � 0 � 2
Directions Write the missing step in solving each equation.
Solve for x: x � 14 � 3 Check: Let x � 17; x � 14 � 3 �� 14 � �14 17 � 14 � 3 � 3 � 3
x � 17 True.
Directions Solve each equation for x. Use the substitution principle tocheck your answers.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. x � 7 � 12
______ � ______
x � 0 � 19
2. x � 9 � 1
______ � ______
x � 0 � �8
3. x � 11 � �33
______ � ______
x � 0 � �44
4. 8.5 � x � 12
______ � ______
0 � x � 3.5
5. x � 1�12� � 14�12
�
______ � ______
x � 0 � 13
6. x � �23� � 5
______ � ______
x � 0 � 5�23
�
7. x � �17� � ��27
�
______ � ______
x � 0 � ��37
�
8. 8�23� � x � 5�13
�
______ � ______
0 � x � �3�13
�
9. x � 10 � 27 ____________________
10. x � 12 � 7 ____________________
11. x � 3�12� � �8 ____________________
12. 19 � x � 9 ____________________
13. �12� � x � �2 ____________________
14. 16 � x � 8 ____________________
15. x � �13� � 9 ____________________
16. �8.7 � x � 12 ____________________
17. x � 0.8 � �2.3 ____________________
18. 5 � x � 20�14� ____________________
19. x � 16.6 � �3.4 ____________________
20. �9�23� � x � �1�13
� ____________________
EXAMPLE
Name Date Period Workbook Activity
Chapter 1, Lesson 44
Solutions by Multiplication or Division
Write how to use the rule for multiplication or division to solve 3x � 18.
Multiply by �13� or divide by 3.
Directions Write how you can use the rule for multiplication or divisionto solve the equation.
1. 6x � 12 multiply by ______ or divide by ______
2. �13�x � 15 multiply by ______ or divide by ______
3. �7x � 21 multiply by ______ or divide by ______
4. �23�x � 15 multiply by ______ or divide by ______
5. ��12�x � 4 multiply by ______ or divide by ______
Solve for x: �12�x � 14 Check: Let x � 28; �12
�x � 14 �
(2)(�12�x) � (2)(14) �12
�(28) � 14 � 14 � 14
x � 28 True.
Directions Solve for x. Use the substitution principle to check your answers.
Directions Solve each problem.
16. 8 times what number equals 24? __________________________________
17. 12 times what number equals 4? __________________________________
18. 25 times what number equals 5? __________________________________
19. �13� of what number is 9? __________________________________
20. �25� of what number is 1? __________________________________
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
6. 9x � 36 _____________________
7. 10x � 50 _____________________
8. 18x � 6 _____________________
9. �7x � 49 _____________________
10. �8x � �4 _____________________
11. �14�x � 2 _____________________
12. ��32�x � 12 _____________________
13. �110�x � 45 _____________________
14. �1,0100�x � 8.35 _____________________
15. ��14�x � �12
� _____________________
EXAMPLE
EXAMPLE
Name Date Period Workbook Activity
Chapter 1, Lesson 55
Multistep Solutions
Directions One step is missing in the solution to each equation.Using a complete sentence, write the missing step.
1. 8x � 18 � 46
Step 1 Add 18 to both sides of the equation.
Step 2 _________________________________________________________________
2. ��14�x � 16 � �4
Step 1 Subtract 16 from both sides of the equation.
Step 2 _________________________________________________________________
3. �15�x � 12 � 18
Step 1 _________________________________________________________________
Step 2 Multiply both sides of the equation by 5 (or divide by �15
�).
4. �23�x � 6 � 24
Step 1 Subtract 6 from both sides of the equation.
Step 2 _________________________________________________________________
Solve for x: 9x � 16 � 43 Check: Let x � 3; 9x � 16 � 43 � 9(3) � 16 � 43 �9x � 16 � 43 27 � 16 � 43 � 43 � 43
9x � 16 � 16 � 43 � 16 True.9x � 27
(�19�)(9x) � (27)(�19
�)x � 3
Directions Solve each equation. Use the substitution principle to checkyour answers.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
5. 5x � 3 � 18 __________________
6. 30 � 5x � 0 __________________
7. 17 � 3x � 11 __________________
8. 22x � 5 � 93 __________________
9. 7 � 4x � 11 __________________
10. 3 � 6x � 21 __________________
11. 4x � 10 � 26 __________________
12. �3x � 7 � �14 __________________
13. �12�x � 12 � 16 __________________
14. 35 � �23�x � 13 __________________
15. ��110�x � 8 � 46 __________________
16. �45�x � 4 � 8 __________________
17. ��27�x � 6 � �4 __________________
18. �9x � 9 � �9 __________________
19. ��56�x � 3 � 27 __________________
20. �53�x � 18 � �43 __________________
EXAMPLE
Axioms of Inequality and Real Number Line
Directions On the line beside each inequality, write the letter of thegraph from the right column that matches the inequality.
1. ____________ 4 � x � 0 A
2. ____________ x � 2 � 0 B
3. ____________ 3x � 6 � 0 C
4. ____________ 18 � 6x � 0 D
5. ____________ 4x � 4 � 0 E
6. ____________ �2 � x � 0 F
7. ____________ 100 � 20x � 0 G
Solve for x. Graph the solution.8 � 2x � 0
8 � 2x � 8 � 0 � 8�2x � �8
(��12�)(�2x) � (�8)(��12
�)x � 4
Directions Solve each inequality for x. Graph each solution on the number line provided.
8. x � 6 � 0
9. 12x � 48 � 0
10. 9x � 18 � 0
11. �12�x � 8 � 0
12. �24 � 6x � 0
13. 25 � 100x � 0
14. 45x � 90 � 0
15. ��43�x � 16 � 0
2 3 4 5 6 7 8 9
�4 �3�2 �1 0 1 2 3
2 3 4 5 6 7 8 9
�6 �5�4 �3�2 �1 0 1
0 1 2 3 4 5 6 7
Name Date Period Workbook Activity
Chapter 1, Lesson 66
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
�4 �3�2 �1 0 1 2 3
0 1 2 3 4 5 6 7
�6�5 �4 �3 �2 �1 0 1
EXAMPLE
Name Date Period Workbook Activity
Chapter 1, Lesson 77
Comparing Pairs of Numbers
Directions For each ordered pair of numbers, write whether y � x, y � x,or y � x.
(3, 5) lies above the equals line.
(�2, �2) lies on the equals line.
(�1, �2) lies below the equals line.
Directions Write above, below, or on to tell where each point lies in relation to the equals line on the coordinate plane.
Directions Write a value for the missing coordinate in each pair to makeeach statement true.
22. (�3, ___) lies on the equals line.
23. (___, �6) lies above the equals line.
24. (0, ___) lies below the equals line.
25. (___, �18) lies below the equals line.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
10. (�2, 3) ____________
11. (7, �4) ____________
12. (0, 4) ____________
13. (8, �8) ____________
14. (�3, �3) ____________
15. (0, 0) ____________
16. (�4, 2) ____________
17. (�14, �12) ____________
18. (7.2, �6.9) ____________
19. (�42, �50) ____________
20. (102, 102) ____________
21. (��12�, ��34
�) ____________
1. (4, �1) ____________
2. (�5, 6) ____________
3. (�4, �4) ____________
4. (�2, 3) ____________
5. (�8, �7) ____________
6. (19, �19) ____________
7. (�12�, ��14
�) ____________
8. (3�12�, �4) ____________
9. (�3, 2.5) ____________
EXAMPLES
x –4 –3 –2 –1 1 2 3 4
5
4
3
2
1
–1
–2
–3
–4
y(3, 5)
(–2, –2) (–1, –2)• •
•
Name Date Period Workbook Activity
Chapter 1, Lesson 88
Intervals on the Real Number Line
Directions On the line beside each inequality, write the letter of thegraphed interval from the right column that matches theinequality.
1. ____________ x � 1 or x � 3 A
2. ____________ �3 x 3 B
3. ____________ x � 2 or x � 2 C
4. ____________ x �3 or x 1 D
5. ____________ 0 x 4 E
6. ____________ x � 4 or x � 0 F
7. ____________ �3 � x � 1 G
Write an inequality for the interval shown.
3 x �4
Directions Write an inequality for each interval.
8. ____________________________
9. ____________________________
10. ____________________________
11. ____________________________
12. ____________________________
13. ____________________________
14. ____________________________
15. ____________________________
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
2 3 4 5 6 7 8 9
�4 �3�2 �1 0 1 2 3
�2 �1 0 1 2 3 4 5
�5�4 �3�2 �1 0 1 2 3 4 5
�4 �3 �2 �1 0 1 2 3
�2 �1 0 1 2 3 4 5
�4 �3 �2�1 0 1 2 3
�2 �1 0 1 2 3 4 5
�2 �1 0 1 2 3 4 5
�4 �3�2 �1 0 1 2 3
�4 �3�2 �1 0 1 2 3
�2 �1 0 1 2 3 4 5
�10�9�8�7�6 �5�4 �3�2
�5 �4�3�2�1 0 1 2 3 4 5
�4 �3�2�1 0 1 2 3
�10�9�8�7�6 �5�4 �3 �2
EXAMPLE
Name Date Period Workbook Activity
Chapter 1, Lesson 99
Solutions of Absolute Value Equations
For |x| � 15, x � 15 or x � �15.
Directions Write all the values for x that make each statement true.
For |x � 6| � 8, x � 6 � 8 or x � 6 � �8.
Directions Write the two equations that you need to solve to find thesolution of each absolute value equation.
6. |x � 3| � 6 _____________________ or _____________________
7. |x � 9| � 5 _____________________ or _____________________
8. |x � �12�| � 4 _____________________ or _____________________
9. |x � 3�14�| � 7�34
� _____________________ or _____________________
10. |x � 1.3| � 8.5 _____________________ or _____________________
|x| � 8 |x � 2| � 10 |4x � 1| � 15x � 8 or x � �8 x � 2 � 10 or x � 2 � �10 4x � 1 � 15 or 4x � 1 � �15
x � 2 � 2 � 10 � 2 or 4x � 1 � 1 � 15 � 1 or x � 2 � 2 � �10 � 2 4x � 1 � 1 � �15 � 1x � 8 or x � �12 4x � 16 or 4x � �14
(�14�)(4x) � (16)(�14
�) or (�14�)(4x) � (�14)(�14
�)
x � �146� � 4 or x � ��4
14� � �3�12�
Directions Solve for x. Use the substitution principle to check your answers.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
1. |x| � 9 x � _____ or x � _____
2. |x| � 7 x � _____ or x � _____
3. |x| � 42 x � _____ or x � _____
4. |x| � 2�12� x � _____ or x � _____
5. |x| � �14� x � _____ or x � _____
11. |x| � 25 ____________________
12. |x � 6| � 10 ____________________
13. |x � 17| � 25 ____________________
14. |2x � 3| � 5 ____________________
15. |7x � 2| � 12 ____________________
16. |12 � 4x| � 16 ____________________
17. |3x � 10| � 17 ____________________
18. |65 � 5x| � 10 ____________________
19. |17x � 1| � 0 ____________________
20. |�23�x � 4| � 18 ____________________
EXAMPLE
EXAMPLE
EXAMPLES
Name Date Period Workbook Activity
Chapter 1, Lesson 1010
Solutions of Absolute Value Inequalities
Directions On the line beside each absolute value inequality, write theletter of the graph from the right column that matches theinequality.
1. ____________ |x � 2| 5 A
2. ____________ |x � 3| � 1 B
3. ____________ |2x � 1| 3 C
4. ____________ |3x � 6| � 0 D
5. ____________ |4x � 4| � 12 E
6. ____________ |x � 1| 1 F
7. ____________ |10x � 5| � 15 G
8. ____________ |4x � 2| � 6 H
Solve for x. Graph.|5x � 10| 10
5x � 10 10 or 5x � 10 �105x � 10 � 10 10 � 10 or 5x � 10 � 10 �10 � 10
5x 0 or 5x �20
(�15�)(5x) (�15
�)(0) or (�15�)(5x) (�15
�)(�20)
x 0 or x �4
Directions Solve each inequality for x. Graph each solution on the number line provided.
9. |x| 5
10. |3x| � 9
11. |12x| 36
12. |x � 1| � 4
13. |x � 5| 10
14. |4x � 8| � 12
15. |�12�x � 4| � 2
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
�4 �3�2 �1 0 1 2 3
�2�1 0 1 2 3 4 5
�3�2 �1 0 1 2 3 4 5
�10�8�6�4 �2 0 2 4 6
�6 �5�4 �3�2 �1 0 1 2
�6�4�2 0 2 4 6 8
�4 �3�2 �1 0 1 2 3
�4�3 �2 �1 0 1 2 3
EXAMPLE�5 �4�3 �2 �1 0 1 2 3
Name Date Period Workbook Activity
Chapter 1, Lesson 1111
Geometry Connection: Relating Lines
�1 x 2 x 1 3 x 3
Directions Draw a geometric picture that fits with each algebra statement. Tell whether the picture is a line, ray, or segment.
Directions Write whether the graph of the solution set of each equationor inequality below is a point, two points, a line, a ray, tworays, or a segment.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
11. x 4 ______________________
12. x �45 ______________________
13. |x| 1 ______________________
14. x ��43� ______________________
15. |x| 0 ______________________
16. |x| 8 ______________________
17. x � 2 � 7 ______________________
18. |x � 2| � 7 ______________________
19. x � 2 5 ______________________
20. |x| � 12 ______________________
21. |x| 5 ______________________
22. |x � 3| � 7 ______________________
23. |x � 3| 7 ______________________
24. 3x � 5 � 13 ______________________
25. 3x � 5 13 ______________________
26. |3x � 5| 13 ______________________
27. |3x � 5| 13 ______________________
28. x � 3 � 3 ______________________
29. 6 � 2x � 10 ______________________
30. 6 � 2x 10 ______________________
�2�1 0 1 2 0 1 2 3 4 1 2 3 4 5
segment ray lineEXAMPLES
1. x 4 ________________
2. x 3 or x �3 ________________
3. x 0 or x 0 ________________
4. �3 x 20 ________________
5. x 57 ________________
6. 1 x 100 ________________
7. x �0.783 or x 0.783________________
8. x 100 or x 100 ________________
9. x �5.6 ________________
10. �99 x 10 ________________
Name Date Period Workbook Activity
Chapter 2, Lesson 112
Functions as Ordered Pairs
Is this set of ordered pairs a function?(5, 4), (7, 2), (9, 0), (11, �2)The set of ordered pairs is a function because no x-coordinates have been repeated.
Directions Tell whether the sets of ordered pairs are functions or not.Write yes or no and explain your answer.
Directions If a vertical line passes through two or more points of a graph,the graph does not represent a function. Use this vertical linetest to determine if the graph is a function or not.Write yes or no.
Write the domain and range of this function.(7, �2), (1, 4), (3, 6), (�4, �1)The domain is 7, 1, 3, �4. The range is �2, 4, 6, �1.
Directions Write the domain and range for each function below.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. (1, 0), (4, 2), (7, 4), (10, 6)
____________________________________
2. (5, �2), (5, �1), (5, 0), (5, 1)
____________________________________
3. (�3, 3), (�2, 2), (�1, 1), (0, 0)
____________________________________
4. (9, �2), (8, 1), (7, 4), (6, 7)
____________________________________
5. (0, 0), (�1, 2), (1, 0), (1, 2)
____________________________________
EXAMPLE
8. (1, �2), (0, 2), (�1, 6), (�2, 10) ________
9. (5, 0), (3, �2), (1, �4), (�1, �6) ________
10. (0, 4), (2, �1), (4, �6), (�2, 8) ________
6. 7.
x –4 –3 –2 –1 1 2 3 4
5
4
3
2
1
–1
–2
–3
–4
y
•
•
•x
–8 –6 –4 –2 2 4 6 8
8
6
4
2
–2
–4
–6
–8
y
• •••
Name Date Period Workbook Activity
Chapter 2, Lesson 213
Functions as a Rule
Calculate f(x) for the given domain values.f(x) � 3x; x � 1, 3, 8, 10, 100f(x) � 3, 9, 24, 30, 300 for the given domain values.
Directions Calculate f(x) for the given domain values.
Choose any number; then multiply it by 7.
f(x) � 7x is a rule in function notation for the example above. The reason that it is a function is that each x has one and only one 7x.
Directions Write a rule using function notation, f(x) � _____.Then give a reason why it is a function.
11. Choose any number; then divide it by 6. _____________________________
12. Choose any number; then multiply it by 4. _____________________________
13. Choose any number; multiply it by 3, then add 15. _____________________________
14. Choose any number; then subtract 9. _____________________________
15. Choose any number; then divide it by �2. _____________________________
16. Choose any number; then multiply it by �5. _____________________________
17. Choose any number; multiply it by �8, then subtract 7. _____________________________
18. Choose any number; divide it by 3, then add 13. _____________________________
19. Choose any number; multiply it by 4, then subtract 52. _____________________________
Directions Solve the problem.
20. Each month Daisy shoots eight rolls of film. Write a rule that showshow many rolls of film she shoots for a given number of months.Write the rule in function notation.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. f(x) � 5x; x � 4, 6, 8, 10, 20
2. f(x) � �3x; x � 0, �1, �2, �3, �4
3. f(x) � �16�x; x � 6, 12, �12, �42, 60
4. f(x) � 5x � 2; x � 0, 1, 2, 3, 4
5. f(x) � 7x � 11; x � 3, 6, 9, 12, 15
6. f(x) � �12�x � 5; x � 0, 4, 10, 50, �100
7. f(x) � 4x � 8; x � 1, 11, 21, 31, 101
8. f(x) � �2x � 14; x � �1, �5, �10, �15, 12
9. f(x) � �13�x � 22; x � 9, 6, 3, 0, �3
10. f(x) � �78�x � 12; x � 16, 24, 48, �8, �64
EXAMPLE
Name Date Period Workbook Activity
Chapter 2, Lesson 314
Zeros of a Function
f(x) � 3x � 6 Find the zeros of f(x).
Let f(x) � 0 and solve for x.0 � 3x � 66 � 3x2 � x
Check: f(2) � 3(2) � 6f(2) � 6 � 6f(2) � 0
Directions Find the zeros of f(x).
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. f(x) � �2x � 12 __________________
2. f(x) � �25�x � 10 __________________
3. f(x) � 4x � 4 __________________
4. f(x) � �13�x � 9 __________________
5. f(x) � x � 8 __________________
6. f(x) � x2 � 64 __________________
7. f(x) � �14�x � 3 __________________
8. f(x) � 5x � 10 __________________
9. f(x) � �x � 8 __________________
10. f(x) � 6x � 42 __________________
11. f(x) � 9x � 9 __________________
12. f(x) � 7x � 3 __________________
13. f(x) � �38�x � 1 __________________
14. f(x) � x2 � 81 __________________
15. f(x) � 8x � 4 __________________
16. f(x) � �27�x � 4 __________________
17. f(x) � x3 � 125 __________________
18. f(x) � �34�x � 12 __________________
19. f(x) � 10x � 25 __________________
20. f(x) � x3 � 27 __________________
21. f(x) � 2x � 10 __________________
22. f(x) � �110�x � 100 __________________
23. f(x) � 7x � 91 __________________
24. f(x) � 6x �15 __________________
25. f(x) � �1201�x � 1 __________________
26. f(x) � 30x � 450 __________________
27. f(x) � x4 � 81 __________________
28. f(x) � �16�x � 2 __________________
29. f(x) � 15x � 75 __________________
30. f(x) � x5 � 32 __________________
Name Date Period Workbook Activity
Chapter 2, Lesson 415
Graphs of Linear Functions
Graph f(x) � 3x � 5.
Step 1 Let x � 0.f(0) � 3(0) � 5 � 5 � (0, 5) is point A.y � 5 is the y-intercept.
Step 2 Let x � �1.f(�1) � 3(�1) � 5 � 2 � (�1, 2) is point B.
Step 3 Graph the two points; then draw the line y � f(x) � 3x � 5.
Directions Graph each linear function and label the y-intercept.(Use graph paper. Label the x- and y-axes first.)
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
x –8 –6 –4 –2 2 4 6 8
8
6
4
2
–2
–4
–6
–8
y
••
A
B
1. f(x) � 2x
2. f(x) � 3x � 2
3. f(x) � �4x
4. f(x) � 2x � 4
5. f(x) � 5x � 1
6. f(x) � �14�x
7. f(x) � �3x � 8
8. f(x) � 2x � 7
9. f(x) � �38�x � 2
10. f(x) � 5x � 2
11. f(x) � �27�x
12. f(x) � 4x � 5
13. f(x) � ��15�x � 3
14. f(x) � x � 10
15. f(x) � �14�x � 6
16. f(x) � 6x � 6
17. f(x) � �170�x
18. f(x) � 10x � 8
19. f(x) � �15�x � 2
20. f(x) � 8x � 8
Name Date Period Workbook Activity
Chapter 2, Lesson 516
The Slope of a Line, Parallel Lines
Calculate the slope of f(x) � 3x � 4.
Step 1 Find two points.
f(1) � 3(1) � 4 � 7 � (1, 7) is point 1.f(0) � 4(0) � 4 � 4 � (0, 4) is point 2.
Directions Calculate the slope of each line. Remember, m � �((
x
y1
1
�
�
y
x2
2
)
)�.
Given f(x) � 5x and g(x) � 5x � 4, show that the lines are parallel by showing that their slopes are equal.
f(1) � 5(1) � 5 � (1, 5) is point 1. g(1) � 5(1) � 4 � 1 � (1, 1) is point 1.f(0) � 5(0) � 0 � (0, 0) is point 2. g(0) � 5(0) � 4 � �4 � (0, �4) is point 2.
m � �((51
��
00))
� � �51
� m � �((11 �
�40))
� � �51
�
m � 5 m � 5
Directions Show that the lines are parallel by showing that their slopesare equal.
Directions Solve the problem.
25. A hill has a height of 450 feet. The horizontal distance covered between thebottom of the hill and the top is 1,800 feet. Find the slope of the hill.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. f(x) � x � 5 __________________
2. f(x) � 4x � 2 __________________
3. f(x) � �3x __________________
4. f(x) � 5x __________________
5. f(x) � �2x � 7 __________________
6. f(x) � �12�x __________________
7. f(x) � �37�x � 5 __________________
8. f(x) � �7x � 2 __________________
9. f(x) � ��29�x � 1 __________________
10. f(x) � x � 6 __________________
11. f(x) � �25�x � 1 __________________
12. f(x) � 2�12�x � 6 __________________
13. f(x) � �4x � 9 __________________
14. f(x) � ��115�x � 3 __________________
15. f(x) � 10x � 1 __________________
16. f(x) � �15x � 25 __________________
17. f(x) � �125�x � 8 __________________
18. f(x) � �4x � 11 __________________
19. f(x) � ��181�x � 5 __________________
20. f(x) � 18x � 1 __________________
21. f(x) � 2x � 5 and g(x) � 2x ______
22. f(x) � �6x and g(x) � �6x � 7 ______
23. f(x) � �13�x � 4 and g(x) � �13
�x � 4 ______
24. f(x) � �x � 100 and g(x) � �x � 8 ______
EXAMPLE
Step 2 Calculate m � �((xy
1
1
�
�
xy2
2
))
�.
m � �((71
��
40
))
� � �31
� � 3
m � 3
Name Date Period Workbook Activity
Chapter 2, Lesson 617
The Formula f(x) � y � mx � b
5x � y � 2 Change to y � mx � b. Give m and b.Solution: Subtract 5x from both sides. y � �5x � 2
m � �5, y-intercept � 2
Directions Change the given equation to the form y � mx � b.Give the value of m and b.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. 2x � 4y � 8 __________________
2. �2x � y � 1 __________________
3. �4x � 4y � 4 __________________
4. �x � 3y � 9 __________________
5. 3x � y � �7 __________________
6. �2x � 2y � 2 __________________
7. x � 4y � 2 __________________
8. �3x � 6y � 12 __________________
9. 4x � 8 � y __________________
10. �6x � 10 � y __________________
11. �6x � 3y � 9 __________________
12. ��13�x � 6y � 2 __________________
13. �25�x � �15
�y � 5 __________________
14. �x � �13�y � 4 __________________
15. �3x � �15�y � �4 __________________
16. 2x � �15�y � 0 __________________
17. x � �110�y � 1 __________________
18. �15�x � 2y � 8 __________________
19. �10x � 8 � 5y � 2 __________________
20. �13�x � 9 � �13
�y � 6 __________________
21. �x � �34�y � �2 __________________
22. �6x � 9y � 3 __________________
23. x � �18�y � �4 __________________
24. �3x � y � 6 __________________
25. �12�x � 2y � 8 � 2y __________________
26. x � �16�y � 6 __________________
27. ��110�x � y � 10 __________________
28. �12x � 4y � 2y � 3 __________________
29. �x � y � 0 __________________
30. �x � y � 2 __________________
Name Date Period Workbook Activity
Chapter 2, Lesson 718
Reading Line Graphs: Slopes of Lines
The slope of this line is positive because it ascends to the right.The y-intercept is 8 because the line crosses the y-axis at (0, 8).The zero or root is �2 because the line crosses the x-axis at (�2, 0).
Directions Give the slope (positive, zero, or negative), the y-intercept,and the zero or root for each graph.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. _______________
2. _______________
3. _______________
4. _______________
5. _______________
6. _______________
7. _______________
8. _______________
9. _______________
10. _______________
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –20 –15 –10 –5 5 10 15 20
20
15
10
5
–5
–10
–15
–20
y
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –8 –6 –4 –2 2 4 6 8
8
6
4
2
–2
–4
–6
–8
y
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –20 –15 –10 –5 5 10 15 20
20
15
10
5
–5
–10
–15
–20
y
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –20 –15 –10 –5 5 10 15 20
20
15
10
5
–5
–10
–15
–20
y
x –8 –6 –4 –2 2 4 6 8
8
6
4
2
–2
–4
–6
–8
y
Name Date Period Workbook Activity
Chapter 2, Lesson 819
Writing Equations of Lines
Write the equation of the line with m � 2 and y-intercept � 7.y � 2x � 7
Directions Given m and b, write the equation of the line.
Write the equation of a line passing through (0, 4) and (1, 1).
Step 1 Calculate m. Let (x1, y1) � (0, 4) and (x2, y2) � (1, 1).
m � �((yx
1
1
�
�
yx
2
2
))
� � �((40
��
11))
� � ��31� � �3
m � �3 so y � �3x � b
Step 2 Substitute one point in y � �3x � b and solve for b.(0, 4) � x � 0, y � 4 4 � �3(0) � b4 � 0 � b4 � b
Step 3 Write the equation: y � �3x � 4.
Directions Write the equation of the line passing through the two points.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. m � �3; b � 4 __________________
2. m � 1; b � 3 __________________
3. m � 5; b � �6 __________________
4. m � 8; b � ��12� __________________
5. m � 2; b � �2 __________________
6. m � �15�; b � �5 __________________
7. m � 4; b � 4 __________________
8. m � �1; b � 0 __________________
9. m � 0; b � 4 __________________
10. m � �37�; b � �1 __________________
11. m � 5; b � ��56� __________________
12. m � ��13�; b � 4 __________________
13. m � �2; b � 0 __________________
14. m � 0; b � �5 __________________
15. m � �45�; b � 1�12
� __________________
16. m � 0; b � 1 __________________
17. m � 5�14�; b � �4 __________________
18. m � �110�; b � 0 __________________
19. m � 11; b � 11 __________________
20. m � �4; b � 14 __________________
21. (1, 1) and (2, 6) ________________
22. (1, 4) and (0, 5) ________________
23. (0, 3) and (�1, 4) ________________
24. (2, 4) and (1, 5) ________________
25. (3, 6) and (1, 7) ________________
26. (5, 0) and (4, �1) ________________
27. (�4, 1) and (0, 2) ________________
28. (�10, 2) and (�11, 3) ________________
29. (6, 2) and (2, 6) ________________
30. (1, 1) and (7, 6) ________________
EXAMPLE
Name Date Period Workbook Activity
Chapter 2, Lesson 920
Graphs of y � mx � b, y � mx � b
y � 3x � 2 y 3x � 2 y 3x � 2.
Directions Write the inequality for the shaded region.
Directions Sketch each of the following inequalities in the coordinate plane.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. _____________________
2. _____________________
3. _____________________
4. _____________________
5. _____________________
6. _____________________
7. x 4 8. y � 3 9. y � �4 10. y 4x
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –5 –4 –3 –2 –1 1 2 3 4 5
5
4
3
2
1
–1
–2
–3
–4
–5
y
x –5 –4 –3 –2 –1 1 2 3 4 5
5
4
3
2
1
–1
–2
–3
–4
–5
y
x –5 –4 –3 –2 –1 1 2 3 4 5
5
4
3
2
1
–1
–2
–3
–4
–5
y
x –5 –4 –3 –2 –1 1 2 3 4 5
5
4
3
2
1
–1
–2
–3
–4
–5
y
x –5 –4 –3 –2 –1 1 2 3 4 5
5
4
3
2
1
–1
–2
–3
–4
–5
y
x –5 –4 –3 –2 –1 1 2 3 4 5
5
4
3
2
1
–1
–2
–3
–4
–5
y
x –5 –4 –3 –2 –1 1 2 3 4 5
5
4
3
2
1
–1
–2
–3
–4
–5
y
x –10 –8 –6 –4 –2 2 4 6 8 10
10
8
6
4
2
–2
–4
–6
–8
–10
y
x –5 –4 –3 –2 –1 1 2 3 4 5
5
4
3
2
1
–1
–2
–3
–4
–5
y
Name Date Period Workbook Activity
Chapter 2, Lesson 1021
Geometry Connection: Lines
In algebra’s coordinate plane, the Lines that have the same slope such asx- and y-axes are perpendicular. y � x � 1 and y � x � 1 are parallel.
Directions Write a reason from geometry why each statement is true.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. The line x � 7 is parallel to the y-axis. Why?
2. The line y � �3 is parallel to the x-axis. Why?
3. The vertical lines are parallel to the y-axis.Why?
4. The horizontal lines are parallel to the x-axis.Why?
5. y � 3x � 5 and y � 3x � 2 are parallel. Why?
x
y
x
y
b b••
•• –1 1
1
–1
y = x + 1
y = x – 1
x –8 –6 –4 –2 2 4 6 8
8
6
4
2
–2
–4
–6
–8
y
x = 7
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
y = –3
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
x –5 –4 –3 –2 –1 1 2 3 4 5
5
4
3
2
1
–1
–2
–3
–4
–5
y
y = 3x + 5
y = 3x – 2
b b
x –4 –3 –2 –1 1 2 3 4
4
3
2
1
–1
–2
–3
–4
y
Name Date Period Workbook Activity
Chapter 3, Lesson 122
The Distributive Law—Multiplication
6(x � y) � 6x � 6y
Directions Multiply, using the distributive law.
(2 � 7)(y � x) � 2y � 2x � 7y � 7x� 9y � 9x
Directions Multiply, using the distributive law twice. Simplify by addinglike terms.
(x � 3)(x � y � 8) �x2 � xy � 8x � 3x � 3y � 24 �x2 � xy � 11x � 3y � 24
Directions Multiply.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. 3(8 � 2) ____________________
2. 6(x � y) ____________________
3. a(b � c) ____________________
4. x(a � b � c) ____________________
5. x(3x � 9) ____________________
6. y(x � y3) ____________________
7. x(a � b � c) ____________________
8. x2(x3 � y3) ____________________
9. x4(x � z � y) ____________________
10. x3(5x3 � x2) ____________________
11. (6 � 4)(a � b) ____________________
12. (a � 2)(a � 4) ____________________
13. (x � y)(a � b) ____________________
14. (x � 3)(x � 5) ____________________
15. (y � 4)(y � 4) ____________________
16. (2a � 4)(a � 5) ____________________
17. (x � y)(y � x) ____________________
18. (a � 2b)(4a � b) ____________________
19. (a � b)(a � b) ____________________
20. (x � y)(3x � 3y) ____________________
21. (x � 5)(x � y � 4) ________________
22. (x � y)(6x � y � z) ________________
23. (x � y)(3x2 � 4y � 7) ________________
24. (x � 4)(4x � y � z) ________________
25. (a � b)(3a � 6b � ab) ________________
26. (a � b)(a3 � b2 � 1) ________________
27. (a � b)(a � 2b � 4ab) ________________
28. (x � 3)(3x � y � 8) ________________
29. (x � 4y)(x � y � xy) ________________
30. (x � y)(x � y � 10) ________________
EXAMPLE
EXAMPLE
Name Date Period Workbook Activity
Chapter 3, Lesson 223
The Distributive Law—Factoring
Examples rb � rc � r(b � c)
3yx2 � 6yx � 9y2 � 3y(x2 � 2x � 3y)
Directions Factor the expressions by finding the common factor(s) first.
Factor x2 � 6x � 9.
Step 1 x2 � 6x � 9 � (x � ___)(x � ___)
Step 2 The factors of 9 are 3 and 3; 1 and 9; �3 and �3; and �1 and �9. So the possible factors for x2 � 6x � 9 include (x � 3)(x � 3); (x � 1)(x � 9); (x � 3)(x � 3); and (x � 1)(x � 9).
Step 3 Substitute each set of factors in the product and check.x2 � 6x � 9 � (x � 1)(x � 9)
� x(x � 9) � 1(x � 9)� x2 � 9x � x � 9� x2 � 10x � 9 Incorrect.
x2 � 6x � 9 � (x � 3)(x � 3)� x(x � 3) � 3(x � 3)� x2 � 3x � 3x � 9� x2 � 6x � 9 Correct.
Directions Factor, using the model (x � ___)(x � ___).Check by multiplying.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLES
1. kl � kj ____________________
2. 9x � 6y ____________________
3. x2 � xy � x ____________________
4. xb � xc � xd ____________________
5. 2x2 � 6xy � 4x ____________________
6. ab � ac � a3 ____________________
7. axy � xy2 ____________________
8. 5xy � 10xya ____________________
9. 4x2y � 12xy � 10y2 ____________________
10. g2 � g3 ____________________
11. x2 � 7x � 6 ____________________
12. x2 � x � 6 ____________________
13. x2 � 8x � 15 ____________________
14. x2 � 2x � 15 ____________________
15. x2 � 2x � 8 ____________________
16. x2 � 3x � 18 ____________________
17. x2 � 25 ____________________
18. x2 � 6x � 5 ____________________
19. x2 � 6x � 7 ____________________
20. x2 � 10x � 25 ____________________
EXAMPLE
Name Date Period Workbook Activity
Chapter 3, Lesson 324
Solutions to ax2 � bx � 0
Example Solve for x and check: 2x2 � 8x � 0.
Step 1 Factor: 2x2 � 8x � 0 � 2x(x � 4) � 0
Step 2 Set each factor equal to 0 and solve for x:2x � 0 or x � 4 � 0x � 0 or x � �4
Check: x � 0, 2x2 � 8x � 0 � 2(0)2 � 8(0) � 0 � 0 � 0x � �4, 2x2 � 8x � 0 � 2(�4)2 � 8(�4) � 32 � 32 � 0
Directions Solve for x and check.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. x2 � 12x � 0 __________________
2. x2 � 3x � 0 __________________
3. x2 � 10x � 0 __________________
4. x2 � 25x � 0 __________________
5. x2 � 13x � 0 __________________
6. x2 � 7x � 0 __________________
7. x2 � 19x � 0 __________________
8. x2 � 23x � 0 __________________
9. x2 � 36x � 0 __________________
10. x2 � 45x � 0 __________________
11. 2x2 � 8x � 0 __________________
12. 3x2 � 15x � 0 __________________
13. 4x2 � 4x � 0 __________________
14. 10x2 � 25x � 0 __________________
15. 8x2 � 16x � 0 __________________
16. 6x2 � 21x � 0 __________________
17. 2x2 � 40x � 0 __________________
18. 3x2 � 30x � 0 __________________
19. 4x2 � 36x � 0 __________________
20. 5x2 � 45x � 0 __________________
21. 2x2 � 48x � 0 __________________
22. 3x2 � 48x � 0 __________________
23. 4x2 � 52x � 0 __________________
24. 5x2 � 75x � 0 __________________
25. 6x2 � 90x � 0 __________________
26. 12x2 � 6x � 0 __________________
27. 20x2 � 4x � 0 __________________
28. 15x2 � 3x � 0 __________________
29. 24x2 � 6x � 0 __________________
30. 35x2 � 7x � 0 __________________
Name Date Period Workbook Activity
Chapter 3, Lesson 425
Solutions to x2 � bx � c � 0 by Factoring
Example Solve for x by factoring x2 � 7x � 10 � 0. Then check.
Step 1 Factor: x2 � 7x � 10 � 0(x � __)(x � __) � 0 Think: Factors of 10 are 2, 5, 1, 10.(x � 2)(x � 5) � 0
Step 2 Set each factor equal to 0: x � 2 � 0 or x � 5 � 0Solve for x: x � �2 or x � �5
Check: x � �2, x2 � 7x � 10 � 0 � (�2)2 � 7(�2) � 10 � 4 � 14 � 10 � 0x � �5, x2 � 7x � 10 � 0 � (�5)2 � 7(�5) � 10 � 25 � 35 � 10 � 0
Directions Solve for x by factoring. Check your answers.
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. x2 � 2x � 8 � 0 __________________
2. x2 � 2x � 15 � 0 __________________
3. x2 � 6x � 9 � 0 __________________
4. x2 � 3x � 18 � 0 __________________
5. x2 � 4x � 21 � 0 __________________
6. x2 � 10x � 25 � 0 __________________
7. x2 � 9x � 14 � 0 __________________
8. x2 � 3x � 10 � 0 __________________
9. x2 � 5x � 6 � 0 __________________
10. x2 � 6x � 27 � 0 __________________
11. x2 � 11x � 26 � 0 __________________
12. x2 � 12x � 35 � 0 __________________
13. x2 � 14x � 45 � 0 __________________
14. x2 � 2x � 80 � 0 __________________
15. x2 � 20x � 100 � 0 __________________
16. x2 � 6x � 55 � 0 __________________
17. x2 � 8x � 33 � 0 __________________
18. x2 � 8x � 65 � 0 __________________
19. x2 � 13x � 36 � 0 __________________
20. x2 � 14x � 40 � 0 __________________
21. x2 � 30x � 29 � 0 __________________
22. x2 � 9x � 52 � 0 __________________
23. x2 � 16x � 64 � 0 __________________
24. x2 � 19x � 84 � 0 __________________
25. x2 � 20x � 69 � 0 __________________
26. x2 � 3x � 70 � 0 __________________
27. x2 � 17x � 30 � 0 __________________
28. x2 � x � 56 � 0 __________________
29. x2 � x � 72 � 0 __________________
30. x2 � 3x � 108 � 0 __________________
Name Date Period Workbook Activity
Chapter 3, Lesson 526
Solutions to ax2 � bx � c � 0 by Factoring
Example Solve for x by factoring 2x2 � 6x � 4 � 0. Then check.
Step 1 Factor: 2x2 � 6x � 4 � 0(__x � __)(__x � __) � 0 Factors of 2: 2 and 1Factors of 4: 2, 2, 1, and 4Some trial factors:(2x � 1)(x � 4) � 0 (2x � 2)(x � 2)� 2x(x � 4) � 1(x � 4) � 2x(x � 2) � 2(x � 2)� 2x2 � 8x � x � 4 � 2x2 � 4x � 2x � 4� 2x2 � 9x � 4 � 2x2 � 6x � 4No YesThe factors of 2x2 � 6x � 4 � 0 are (2x � 2) and (x � 2).
Step 2 Set each factor equal to 0: 2x � 2 � 0 or x � 2 � 0Solve for x: 2x � �2 or x � �2 x � �1 or x � �2
Check: Let x � �1 and Let x � �2 and2x2 � 6x � 4 � 0 2x2 � 6x � 4 � 02(�1)2 � 6(�1) � 4 � 0 2(�2)2 � 6(�2) � 4 � 02(1) � 6 � 4 � 0 2(4) � 12 � 4 � 02 � 6 � 4 � 0 8 � 12 � 4 � 00 � 0 0 � 0
Directions Solve each equation by factoring. Check your answers.
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EXAMPLE
1. 2x2 � 7x � 6 � 0 __________________
2. 3x2 � 8x � 4 � 0 __________________
3. 4x2 � 17x � 4 � 0 __________________
4. 6x2 � 12x � 6 � 0 __________________
5. 2x2 � 2x � 4 � 0 __________________
6. 6x2 � 11x � 10 � 0 __________________
7. 2x2 � 2x � 12 � 0 __________________
8. 8x2 � 10x � 3 � 0 __________________
9. 4x2 � 25 � 0 __________________
10. 4x2 � 9x � 5 � 0 __________________
11. 2x2 � 3x � 2 � 0 __________________
12. 12x2 � 9x � 3 � 0 __________________
13. 9x2 � 16 � 0 __________________
14. 4x2 � 4x � 8 � 0 __________________
15. 6x2 � 32x � 10 � 0 __________________
16. 8x2 � 18x � 7 � 0 __________________
17. 6x2 � 3x � 9 � 0 __________________
18. 6x2 � x � 1 � 0 __________________
19. 4x2 � 14x � 8 � 0 __________________
20. 6x2 � 13x � 15 � 0 __________________
21. 6x2 � 22x � 20 � 0 __________________
22. 6x2 � 37x � 6 � 0 __________________
23. 5x2 � 26x � 5 � 0 __________________
24. 4x2 � 13x � 3 � 0 __________________
25. 2x2 � 3x � 9 � 0 __________________
26. 6x2 � 5x � 21 � 0 __________________
27. 6x2 � 3x � 18 � 0 __________________
28. 10x2 � 99x � 10 � 0 __________________
29. 12x2 � 25x � 2 � 0 __________________
30. 15x2 � 14x � 3 � 0 __________________
Name Date Period Workbook Activity
Chapter 3, Lesson 627
Trinomials—Completing the Square
Example monomial one term a, b, cd, e2, and so on binomial two terms x � 7, xy � 2, (x2 � 6)trinomial three terms x2 � 4x � 3, 2x2 � 5x � 2polynomial many terms 3x2 � 7x � 6y � 2z2 � 5
Directions Identify each expression. Write monomial, binominal,trinomial, or polynomial.
Complete the square, given x2 � 10x � ___. Check.
Solution: Find �12� of 10 � 5. Square 5 and add to given expression.
x2 � 10x � 25, perfect square trinomial
x2 � 10x � 25
(x � 5)2
Check: (x � 5)2 � (x � 5)(x � 5) � x(x � 5) � 5(x � 5) � x2 � 5x � 5x � 25 � x2 � 10x � 25
Directions Complete the square. Check by factoring and multiplying.
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EXAMPLE
1. 10x2 __________________
2. x2 � 4 __________________
3. 5x � 4y __________________
4. 5x2 � 6x � 3y � 8 __________________
5. 6x2 � 2x � 9 __________________
6. 2x2 � 5x � 2 __________________
7. 52 __________________
8. 5x2 � 3x __________________
9. 6x2 � 13x � 2 __________________
10. a � b � c � d __________________
11. x2 � 40x ____________________
12. x2 � 30x ____________________
13. x2 � 12x ____________________
14. x2 � 18x ____________________
15. x2 � 26x ____________________
16. x2 � 26x ____________________
17. x2 � 40x ____________________
18. x2 � 22x ____________________
19. x2 � 30x ____________________
20. x2 � 2x ____________________
EXAMPLE
Name Date Period Workbook Activity
Chapter 3, Lesson 728
Solutions by Completing the Square
Example Solve x2 � 12x � 13 � 0 by completing the square.
Solution:x2 � 12x � 13 � 0
x2 � 12x � 13 Change to x � bx � constant.x2 � 12x � 36 � 13 � 36 Complete the square. Add [�12�(b)]
2 to both sides.
(x � 6)2 � 49 Factor.�(x � 6�) 2� � ��49� Take the square root of each side.
x � 6 � �7x � 6 � 7 or x � 6 � �7
x � 1 or x � �13
Check: Let x � 1x2 � 12x � 13 � 0 � 1 � 12 � 13 � 0 � 13 � 13 � 0 � 0 � 0Let x � �13x2 � 12x � 13 � 0 � 169 � 156 � 13 � 0 � 169 � 169 � 0 � 0 � 0
Directions Solve by completing the square. Check your answers.
Solve x2 � 4x � 2 � 0 by completing the square.
Solution:x2 � 4x � 2 � 0
x2 � 4x � 2 Change to x � bx � constant.x2 � 4x � 4 � 2 � 4 Complete the square. Add [�12�(b)]
2 to both sides.
(x � 2)2 � 6 Factor.�(x � 2�)2� � ��6� Take the square root of each side.
x � 2 � ��6�x � 2 � ��6� or x � 2 � ��6�
x � �2 � �6� or x � �2 � �6�
Directions Solve by completing the square. Check your answers. You mayleave expressions for square roots in your answers.
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EXAMPLE
1. x2 � 12x � 11 � 0 __________________
2. x2 � 10x � 9 � 0 __________________
3. x2 � 8x � 20 � 0 __________________
4. x2 � 16x � 28 � 0 __________________
5. x2 � 18x � 19 � 0 __________________
6. x2 � 4x � 12 � 0 __________________
7. x2 � 14x � 9 � 0 __________________
8. x2 � 16x � 10 � 0 __________________
9. x2 � 18x � 11 � 0 __________________
10. x2 � 20x � 12 � 0 __________________
EXAMPLE
Name Date Period Workbook Activity
Chapter 3, Lesson 829
The Quadratic Formula
You can rewrite any quadratic equation that is not in standard form so that it is in standard form, ax2 � bx � c � 0.
10x2 � 15 � �19x; standard form is 10x2 � 19x � 15 � 0.
Directions Rewrite in standard form.
Solve 2x2 � 9x � 4 � 0 by using the quadratic formula x � .a � 2, b � 9, c � 4Substitute in the formula: x �
x �
x �
x �
The roots of the equation are x � ��94� 7� � �
�42� � ��
12
�
or x � ��94� 7� � �
�416� � �4
Check: Let x � ��12�; 2x
2 � 9x � 4 � 0 � 2(��12�)2 � 9(��12�) � 4 � 0 � �
24
� � �92
� � 4 � 0
� �12
� � �92
� � �82
� � 0 � 0 � 0
Let x � �4; 2x2 � 9x � 4 � 0 � 2(�4)2 � 9(�4) � 4 � 0 �32 � 36 � 4 � 0 � 36 � 36 � 0 � 0 � 0
Directions Solve, using the quadratic formula.
�9 � 7�
4
�9 � �49���
4
�9 � �81 ��32���
4
�9 � �92 � 4�(2)(4)����
2(2)
�b � �b2 � 4�ac���
2a
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EXAMPLE
EXAMPLE
1. x2 � �6x � 4 __________________
2. 3x � 6 � 10x2 __________________
3. 2x2 � 2x � 27 __________________
4. 25x � 9 � 11x2 __________________
5. 15x2 � 4x � �18 __________________
6. 2x2 � 26x � 54 __________________
7. 4x2 � 70x � 15 __________________
8. 2x2 � 4 � 5x __________________
9. 5 � 3x2 � 16x __________________
10. 3x2 � x � 36 __________________
11. 6x2 � 19x � 3 � 0 __________________
12. x2 � 5x � 4 � 0 __________________
13. 7x2 � 11x � 6 � 0 __________________
14. 8x2 � 14x � 6 � 0 __________________
15. 2x2 � 2x � 4 � 0 __________________
Name Date Period Workbook Activity
Chapter 3, Lesson 930
Complex Roots
Example Are the roots of 2x2 � 3x � 7 � 0 real or complex?a � 2, b � �3, c � 7Radicand � b2 � 4ac� (�3)2 � 4(2)(7)� 9 � 56 � �47
Radicand � 0, so roots are complex.
Directions Evaluate the radicand b2 � 4ac. Then write if the roots of thegiven equation are real or complex.
Using Gauss’s definition, x � �i, and i � ��1�, substitute i for ��1�:
x �
Factor x �
Substitute i for ��1� x �
x � ��44i� � �i
The solutions are x � �i.
Directions Rewrite each number, using i for ��1�.
Directions Use any method to solve these equations. Write complex rootsusing i for ��1�.
13. x2 � 7x � 3 � 0 __________________
14. 3x2 � 5x � 11 � 0 __________________
15. 2x2 � 3x � 4 � 0 __________________
�i�16��
4
�(��1�)(�16�)��
4
���16���
4
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EXAMPLE
1. 5x2 � 2x � 3 � 0 __________________
2. x2 � 10x � 16 � 0 __________________
3. 4x2 � 5x � 2 � 0 __________________
4. �x2 � 6x � 3 � 0 __________________
5. x2 � 15x � 20 � 0 __________________
6. 3x2 � 5x � 1 � 0 __________________
7. 4x2 � 8x � 12 � 0 __________________
8. x2 � x � 1 � 0 __________________
9. ��17�
10. ��23�
11. ��y�
12. ��81�
EXAMPLE
Name Date Period Workbook Activity
Chapter 3, Lesson 1031
Geometry Connection: Areas
Example Write a formula to find the side of a squarewhose area is 81 cm2. Then solve for the side.Let x � s.
x2 � 81x � ��81�
Take square roots.x � �9
The root x � �9 does not makesense for this problem because lengthcannot be a negative number. �9 is called an extraneous root.Solution: s � 9 cm
Directions Find the sides of each square with the given area.
Write a formula to find the sides of a rectangle whosewidth is 7 cm less than its length, with an area260 cm2. Then solve for l and w.Let x � l and x � 7 � w
260 � x(x � 7)260 � x2 � 7x Solution: x � 20, so l � 20 cm.
0 � x2 � 7x � 260 (x � �13 is an extraneous root.)0 � (x � 20)(x � 13) w � x � 7, w � 20 � 7 � 13 cm
x � 20 � 0 or x � 13 � 0 Check: Area � (20 cm)(13 cm) �x � 20 or x � �13 260 cm2
Directions Find the length and width of the following rectangles.
7. Area � 88 yd2; its width is 3 more than its length. __________________
8. Area � 48 ft2; its width is 8 less than its length. __________________
Directions Find the base and height of the following parallelograms.
9. Area � 117 in.2; its height is 4 less than its base. __________________
10. Area � 105 cm2; its height is 8 more than its base. __________________
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EXAMPLE
1. 10,000 m2 __________________
2. 1,600 ft2 __________________
3. 196 cm2 __________________
4. 900 in.2 __________________
5. 625 in.2 __________________
6. 2,500 yd2 __________________
EXAMPLE
x A � 81 cm2
x
x � 7
A � 260 cm2
Name Date Period Workbook Activity
Chapter 4, Lesson 132
f(x) � ax2 � bx � c, Quadratic Functions
Given f(x) � 3x2 � 4x � 1:
Find the values for f(x) for x � 0, 1, and �1.x � 0: f(0) � 3(0)2 � 4(0) � 1 � 1
independent (x, y) dependentx � 0 (0, 1) f(0) � 1
x � 1: f(1) � 3(1)2 � 4(1) � 1 � 8
independent (x, y) dependentx � 1 (1, 8) f(1) � 8
x � �1: f(�1) � 3(�1)2 � 4(�1) � 1 � 0
independent (x, y) dependentx � �1 (�1, 0) f(�1) � 0
Directions Find the values of f(x) for the given domain values. Completea table like the one at the right, listing x and f(x) values foreach function.
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EXAMPLE
1. f(x) � 3x2 � 4x � 1
x � �2, �1, 0, 1, 2
2. f(x) � x2 � 5x � 4
x � �1, 0, 1, 2, 3
3. f(x) � 2x2 � 5x � 2
x � �2, �1, 0, 1, 2
4. f(x) � 4x2 � 4x � 3
x � �1, ��12
�, 0, �12
�, 1
5. f(x) � x2 � 6x � 5
x � �2, �1, 0, 1, 2
6. f(x) � x2 � x � 12
x � �2, �1, 0, 1, 2
7. f(x) � 4x2 � 10x � 6
x � �1, 0, 1, 2, 3
8. f(x) � 3x2 � 10x � 3
x � �2, �1, 0, 1, 2
9. f(x) � x2 � 10x � 8
x � �1, ��12
�, 0, �12
�, 1
10. f(x) � 6x2 � 12x � 6
x � �2, �1, 0, 1, 2
x y � f(x)
Name Date Period Workbook Activity
Chapter 4, Lesson 233
Graphing f(x) � ax2 and f(x) � �ax2
Graph f(x) � 3x2, domain � all real numbers.
Step 1 Let x � ±3, ±2, ±1, 0.Notice that all the range values are positive except 0 and the graph isabove the x-axis.
Step 2 Sketch curve.
Graph of f(x) � 3x2
Domain � all real numbersRange � 0 and all positive numbersThe curve is a parabola.
Directions Find seven points for each function. Then sketch the parabola.
1. f(x) � 5x2 ______________________________________
2. f(x) � �19�x2 ______________________________________
3. f(x) � �8x2 ______________________________________
4. f(x) � ��19�x2 ______________________________________
5. f(x) � �18�x2 ______________________________________
6. f(x) � �7x2 ______________________________________
7. f(x) � �4x2 ______________________________________
8. f(x) � ��112�x2 ______________________________________
9. f(x) � ��18�x2 ______________________________________
10. f(x) � 15x2 ______________________________________
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EXAMPLEx f(x) � 3x2
�3 3(�3)2 � 27
3 3(3)2 � 27
�2 3(�2)2 � 12
2 3(2)2 � 12
�1 3(�1)2 � 3
1 3(1)2 � 3
0 3(0)2 � 0
30
25
20
15
10
5
–5
–10
y
x –20 –15 –10 –5 5 10 15 20
•
•
•
•
•
••
Name Date Period Workbook Activity
Chapter 4, Lesson 334
Graphing f(x) � ax2 � c
Sketch the graph of f(x) � 2x2 � 8.Tell if the roots are real or complex.
Solution:
Step 1 Think of f(x) � 2x2.
Step 2 Move curve down by 8 to get f(x) � 2x2 � 8.
Directions Sketch the following parabolas. Write whether the roots arereal or complex numbers.
Directions Sketch the parabolas and answer the questions about eachparabola.
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EXAMPLE
1. f(x) � 5x2 � 3 __________________
2. f(x) � �x2 � 15 __________________
3. f(x) � �6x2 � 9 __________________
4. f(x) � 4x2 � 16 __________________
5. f(x) � 4x2 � 5 __________________
6. f(x) � 6x2 � 12 __________________
7. f(x) � 9x2 � 10 __________________
8. f(x) � �5x2 � 5 __________________
9. f(x) � �4x2 � 7 __________________
10. f(x) � 8x2 � 3 __________________
11. Sketch a narrow parabola that spills water andhas a turning point of (0, �4). Will thisparabola have real or complex roots?
____________________________________
12. Sketch a parabola that has a turning point of(0, �6) and complex roots. What else can youinfer about the parabola?
____________________________________
13. Sketch a wide parabola with real roots and aturning point of (0, �10). Is the turning pointa minimum or maximum value for f(x)?
____________________________________
14. Sketch a parabola with complex roots and aturning point of (0, 8). Is the turning point aminimum or maximum value for f(x)?
____________________________________
15. Sketch a narrow parabola that holds waterand has a turning point of (0, 6). Will thisparabola have real or complex roots?
____________________________________
x
8
7
6
5
4
3
2
1
y
–4 –3 –2 –1 1 2 3 4 •
• •
• •
f(x) = 2x2
–1
–2
–3
–4
–5
–6
–7
–8
y
x –4 –3 –2 –1 1 2 3 4
•
• •
• •
f(x) = 2x – 82
Name Date Period Workbook Activity
Chapter 4, Lesson 435
Graphing, Using Roots and the Turning Point
Sketch the graph of f(x) � x2 � x � 6.
Step 1 Find the roots by factoring or using the quadratic formula.
x �
x �
x �
x � ��12� 5� or x � ��12
� 5�
x � �42� � 2 or x � ��26� � �3
Directions Sketch the graphs, using the function and three points: tworoots and the turning point.
Given the roots x � �2 and x � 6, sketch the graph.
Step 1 Graph roots.
Step 2 Find midpoint between roots onx-axis: add x-values and divide by 2.
x � �� 22� 6� � �
42
� � 2
(x-value of turning point and axis of symmetry)
Directions Sketch the graphs, using the given roots to determine the function and the turning point.
�1 � �25���
2
�1 � �1 � 2�4���
2
�1 � �12 � 4�(1)(�6�)����
2(1)
©AGS Publishing. Permission is granted to reproduce for classroom use only. Algebra 2
EXAMPLE
1. f(x) � x2 � 7x � 8
2. f(x) � x2 � 5x � 6
3. f(x) � x2� 3x � 10
4. f(x) � x2 � 6x � 16
5. f(x) � x2 � 4x � 5
6. x � �3, x � 1
7. x � �5, x � 3
8. x � �2, x � 4
9. x � �8, x � �6
10. x � 3, x � 7
Step 3 Determine f(x). Calculate f(x) for x � 2 tofind the y-value of the turning point.Roots of x � �2 and x � 6 mean factorsare (x � 2) and (x � 6).f(x) � (x � 2)(x � 6)
� x2 � 4x � 12f(2) � (2)2 � 4(2) � 12
� 4 � 8 � 12� �16
The turning point is (2, �16).
EXAMPLE
Step 2 Find the x-value of the turning point.
x � ��2ab� � �2
�(11)
� � ��12
�
Step 3 Find the y-value of the turning point. Substitute the x-value into the equation and solve for y.
x � ��12�; f(��12
�) � (��12�)2
� (��12�) � 6
� �14
� � �12
� � 6 � �6�14�
The turning point is (��12�, �6�14
�).
–2
–4
–6
–8
–10
–12
–14
–16
y
x –8 –6 –4 –2 2 4 6 8
•
• •
(2, –16)
(–2, 0) (6, 0)
Name Date Period Workbook Activity
Chapter 4, Lesson 536
Reading Quadratic Graphs
Given f(x) � ax2 � bx � c, x �
Which graph represents the described f(x)?
f(x) has a zero radicand.Solution: If f(x) has a zero radicand, f(x)
has two equal roots; graph B represents the function.
f(x) has a negative radicand.Solution: If f(x) has a negative radicand,
f(x) has complex roots; graph C represents the function.
f(x) has a positive radicand.Solution: If f(x) has a positive radicand,
f(x) has real roots; graph F represents the function.
Directions Read the graphs and determine whether the parabola is afunction. Write function or not a function.
Directions Read the graph. Circle the function that represents the graph.
Directions Read the graph. Decide if the roots are real or complex.Write real or complex.
5. ______________________
�b � �b2 � 4�ac���
2a
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EXAMPLES
1. __________________ 2. __________________
3. A f(x) � �6x2
B f(x) � 6x24. A f(x) � �3x2 � 8
B f(x) � �3x2 � 8
–2
–4
–6
–8
y
x –8 –6 –4 –2 2 4
•
• •
x –2 2 4 6 8 10
4
2
–2
–4
y
•
•
•
x
y
x
y
x
y
x
y
x
y
x
y
BA
DC
FE
x
y
x
y
x
y
Name Date Period Workbook Activity
Chapter 4, Lesson 637
Parabolas and Straight Lines
Find the common solutions to y � f(x) � x2 � 3 and y � 3x � 1.
Step 1 Equate y-values.Equate y � x2 � 3 and y � 3x � 1.x2 � 3 � 3x � 1x2 � 3x � 20 � x2 � 3x � 2
Step 2 Solve for x. Step 3 Substitute in either function.0 � x2 � 3x � 2 x � 2, y � 3x � 1 � y � 3(2) � 1 � 70 � (x � 2)(x � 1) Point A is (2, 7).x � 2 � 0 or x � 1 � 0 x � 1, y � 3(1) � 1 � 4x � 2 or x � 1 Point B is (1, 4).
Directions Find the common solutions. Give the coordinates of points A and B.
Use algebra to show that there are no common solutions toy � f(x) � x2 and y � x � 4.
Step 1 Equate y-values.Equate y � x2 and y � x � 4.x2 � x � 4x2 � x � 4 � 0
Step 2 Solve for x.
x2 � x � 4 � 0
x �
x �
Directions Use algebra to show that there are no common solutions.
1 � i�15���
2
1 � ��15���
2
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EXAMPLE
4. y � f(x) � x2 � 3y � x � 8
5. y � f(x) � x2
y � �4
1. y � f(x) � 2x2
y � 8
_________________
2. y � f(x) � �13�x2
y � x � 6
_________________
3. y � f(x) � �4x2
y � 8x � 12
_________________
EXAMPLE
x
10
8
6
4
2
–2
–4
y
–8 –6 –4 –2 2 4 6 8
y = x – 4
y = f(x) = x 2
x
10
8
6
4
2
–2
–4
y
–8 –6 –4 –2 2 4 6 8
•
•A
B
y = 3x + 1
y = f(x) = x + 32
Step 3 x �
indicates the system of equations has complex roots. The graphs of the functions do not intersect.
1 � i�15���
2
Name Date Period Workbook Activity
Chapter 4, Lesson 738
The Straight Lines
Check if the system of linear equations has a common solution. If it does, find the common solution.
Step 1 Compare the slopes of each line. If they are not equal then they have a common solution.y � 3x � 7 m � 3y � x � 9 m � 1The slopes are not equal. Therefore, the system has a common solution.
Step 2 Elimination MethodEquate y from the equations.Rewrite y � 3x � 7 as y � 3x � 7Rewrite y � x � 9 as y � x � �9Subtract to eliminate y. y � 3x � 7
y � x � �9y � y � 3x � (�x) � 7 � (�9)
�2x � 16x � �8
Step 3 Use this value of x to find the corresponding value of y.x � �8, y � 3x � 7 � y � 3(�8) � 7 � �17 x � �8, y � x � 9 � y � (�8) � 9 � �17Common solution: (�8, �17)
Directions Determine whether the system has a common solution.Write yes or no.
Directions Find the common solution for each system of equations.
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EXAMPLE
7. y � 4x � 2 _________________y � 2x � 3
8. 4y � 4x � 8 _________________y � 2x � 4
9. 2y � 4x � 12 _________________3x � y � 5
10. 5x � 6 � y _________________4x � 7 � y
1. y � 2x � 4 _________________y � 4x � 2
2. 3y � x � 6 _________________y � 3x
3. 2x � 8 � y _________________y � 2x � 6
4. 3x � 6y � 4 _________________5x � 3y � 6
5. y � 12 � 3x _________________y � 3x � 6
6. 9x � 3y � 6 _________________8y � 16x � 2
Name Date Period Workbook Activity
Chapter 4, Lesson 839
Word Problems and Linear Equations
The sum of two numbers is 26, and their difference is 8. What are the numbers?
Solution: Let x � one number, y � the other numberx � y � 26 Sum is 26.x � y � 8 Difference is 8.
Add the equations: x � y � 26x � y � 8
2x � 0 � 34x � 17
Substitute: x � y � 26 � 17 � y � 26 � y � 9
Common solution is (17, 9).Check: 17 � 9 � 26, 17 � 9 � 8 True.
Directions Solve.
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EXAMPLE
1. The sum of two numbers is 34. The differenceof the two numbers is 12. What are thenumbers?
________________________________
2. The sum of two numbers is 83. The differenceof the two numbers is 17. What are thenumbers?
________________________________
3. The sum of two numbers is 62. The differenceof the two numbers is 18. What are thenumbers?
________________________________
4. The sum of two numbers is 57. The differenceof the two numbers is 11. What are thenumbers?
________________________________
5. The sum of two numbers is 88. The differenceof the two numbers is 32. What are thenumbers?
________________________________
6. You have 27 coins consisting of pennies andnickels. The coins total $0.83. How manycoins are pennies? How many are nickels?
________________________________
7. You have 31 coins consisting of nickels anddimes. The coins total $2.25. How many coinsare nickels? How many are dimes?
________________________________
8. You have 59 coins consisting of pennies andnickels. The coins total $2.87. How manycoins are pennies? How many are nickels?
________________________________
9. You have 67 coins consisting of dimes andnickels. The coins total $3.95. How manycoins are dimes? How many are nickels?
________________________________
10. You have 24 coins consisting of dimes andquarters. The coins total $3.15. How manycoins are dimes? How many are quarters?
________________________________
Name Date Period Workbook Activity
Chapter 4, Lesson 940
Geometry Connection: Axis of Symmetry
Matching points must be equidistant from the axis of symmetry.
l1 is an axis of symmetry. l2 is not an axis of symmetry.
Directions Which is an axis of symmetry for the given figure? Write l1 or l2.
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EXAMPLES
1. __________________
2. __________________
3. __________________
4. __________________
5. __________________
l2
l1
l1
l2
l1
l2
l1
l2
l1
l2
l1
l2
Name Date Period Workbook Activity
Chapter 5, Lesson 141
Definitions, Addition
Add 5x3 � 9x2y � 7xy2 � 2x � 15 and 4x2y2 � x2y � 8xy2 � 5x �10.
Group like terms, then add.
5x3 � 9x2y � 7xy2 � 2x � 15
� 4x2y2 � x2y � 8xy2 � 5x � 10
5x3 � 4x2y2 � 10x2y � xy2 � 3x � 5
Directions Add the expressions.
1. x4y2 � 6x2y � 3xy2 and 3x3y2 � 8x2y � xy2 � 10x
__________________________________________
2. 3x3y2 � 8x2y � 12xy � 16x � 10 and 4x3y2 � 7x2y � 6xy � 4y2 � 4
__________________________________________
3. 9x4y3 � 3x3y2 � 7x2y � 6y3 � 6y2 � 18 and 12x3y2 � 14x2y � 7y2 � 11
__________________________________________
4. 3x4y2 � 6x3y2 � 7x2y2 � 10xy2 � 14y � 17 and �7x3y2 � 7x2y2 � 19xy2 � y � 4
__________________________________________
5. 10x4y3 � 7x3y3 � 16x2y � 8xy3 � 7xy � 2 and 4x3y3 � 8x2y � 8xy3 � 6xy � 12
__________________________________________
Directions: Find the difference.
6. Subtract 3x3y2 � 8x2y � xy2 � 10x from x4y2 � 6x2y � 3xy2.
__________________________________________
7. Subtract 4x3y2 � 7x2y � 6xy � 4y2 � 4 from 3x3y2 � 8x2y � 12xy � 16x � 10.
__________________________________________
8. Subtract 12x3y2 � 14x2y � 7y2 � 11 from 9x4y3 � 3x3y2 � 7x2y � 6y3 � 6y2 � 18.
__________________________________________
9. Subtract �7x3y2 � 7x2y2 � 19xy2 � y � 4 from 3x4y2 � 6x3y2 � 7x2y2 � 10xy2 � 14y � 17.
__________________________________________
10. Subtract 4x3y3 � 8x2y � 8xy3 � 6xy � 12 from 10x4y3 � 7x3y3 � 16x2y � 8xy3 � 7xy � 2.
__________________________________________
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EXAMPLE
Name Date Period Workbook Activity
Chapter 5, Lesson 242
Products: (a � b)2, (a � b)2, (a � b)3, (a � b)3
Find (2x � 4y)2.Model method: (a � b)2 � a2 � 2ab � b2
Let a � 2x, b � �4y.(2x � 4y)2 � (2x)2 � 2(2x)(�4y) � (�4y)2
� 4x2 � 16xy � 16y2
Directions Write the expressions in expanded form.
Find (3x � y)3.
Factor method:(3x � y)3 � (3x � y)(3x � y)2
� (3x � y)(9x2 � 6xy � y2)� 3x(9x2 � 6xy � y2) � y(9x2 � 6xy � y2)� 27x3 � 18x2y � 3xy2 � 9x2y � 6xy2 � y3
� 27x3 � 27x2y � 9xy2 � y3
Model method: (a � b)3 � a3 � 3a2b � 3ab2 � b3
Let a � 3x, b � �y.(3x � y)3 � (3x)3 � 3(3x)2(�y) � 3(3x)(�y)2 � (�y)3
� 27x3 � 27x2y � 9xy2 � y3
Directions Write the expressions in expanded form.
11. (y � z)3 ___________________________
12. (3x � 4)3 ___________________________
13. (2x � y)3 ___________________________
14. (3x � 2y)3 ___________________________
15. (5x � 3y)3 ___________________________
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EXAMPLE
1. (2x � 6)2 _____________________
2. (3x � 4)2 _____________________
3. (5x � 1)2 _____________________
4. (3x � 2y)2 _____________________
5. (4m � 4n)2 _____________________
6. (3a � 4b)2 _____________________
7. (6x � 6y)2 _____________________
8. (q � 5r)2 _____________________
9. (4t � 3v)2 _____________________
10. (8x � y)2 _____________________
EXAMPLE
Name Date Period Workbook Activity
Chapter 5, Lesson 343
Factoring a2 � b2, a3 � b3, and a3 � b3
Find the factors of 4x2 � 4y2.Solution: Use the model a2 � b2 � (a � b)(a � b).Let a � 2x, b � 2y; then 2x2 � 2y2 � (2x � 2y)(2x � 2y).
Find the factors of y3 � z3.Solution: Use the model a3 � b3 � (a � b)(a2 � ab � b2).Let a � y, b � z; then y3 � z3 � (y � z)(y2 � yz � z2).
Factor x3 � 8.Solution: Use the model a3 � b3 � (a � b)(a2 � ab � b2).Let a � x, b � 2; then x3 � 8 � (x � 2)(x2 � 2x � 4).
Directions Find the factors. Use a model.
1. m2 � n2 __________________________
2. 9x2 � y2 __________________________
3. 16x2 � 4y2 __________________________
4. 100x2 � 25y2 __________________________
5. 49m2 � 64n2 __________________________
6. 8x3 � y3 __________________________
7. p3 � r3 __________________________
8. x3 � 27y3 __________________________
9. 8x3 � 64y3 __________________________
10. 125s3 � 8t3 __________________________
11. t3 � w3 __________________________
12. 8x3 � 8y3 __________________________
13. 64a3 � 8 __________________________
14. 27 � b3 __________________________
15. 216a3 � 125b3 __________________________
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EXAMPLES
Name Date Period Workbook Activity
Chapter 5, Lesson 444
Multiplication of Polynomials
Multiply the polynomials. Simplify and write the answer alphabeticallyand in descending order of the power of the terms.
(x � 3y)(x3 � 4x � 8)� x(x3 � 4x � 8) � 3y(x3 � 4x � 8)� x 4 � 4x2 � 8x � 3x3y � 12xy � 24y� x 4 � 3x3y � 4x2 � 8x � 12xy � 24y
(x � y)2(4x � y)2
� (x2 � 2xy � y2)(16x2 � 8xy � y2)� x2(16x2 � 8xy � y2) � 2xy(16x2 � 8xy � y2) � y2(16x2 � 8xy � y2)� 16x 4 � 8x3y � x2y2 � 32x3y � 16x2y2 � 2xy3 � 16x2y2 � 8xy3 � y 4
� 16x 4 � 24x3y � x2y2 � 6xy3 � y 4
Directions Multiply. Write the answer alphabetically in descending orderof the power of the terms.
1. (x2 � 3)(x3 � 2x) _______________________________
2. (2x � 4y)(x3 � x) _______________________________
3. (5x2 � 4)(x2 � 15) _______________________________
4. (x3 � 7x2 � 2)(x � y) _______________________________
5. (8x2 � y)(x � 2y � 7y2) _______________________________
6. (3x3 � y)(x2 � 2x � 4y � 1) _______________________________
7. (4x2 � 4)(6y2 � 2x � 3) _______________________________
8. (x � 3)(x2 � xy � y2) _______________________________
9. (3x � 2y)(x � 3y � 8y2) _______________________________
10. (x2 � 7)(x2 � 2xy2 � 3) _______________________________
11. (x � 4y � 8z)(4x � 9y � 7z) _______________________________
12. (x3 � 2x2y � 2y)(x2 � 3y � 2) _______________________________
13. (3x � y)(x2 � 3xy � 4) _______________________________
14. (7x � 2y � 8z)(2x � 4z) _______________________________
15. (2x2 � 4x)(x � 3y2 � 7y) _______________________________
16. (4x3 � 2y2 � 12)(2x � 3y2) _______________________________
17. (x2 � 7xy � 4y)(x2 � 5xy) _______________________________
18. (x � 3y)2(5x � 2y) _______________________________
19. (3x � 5)2(2x � y) _______________________________
20. (4x � y)2(x � y)2 _______________________________
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EXAMPLES
Name Date Period Workbook Activity
Chapter 5, Lesson 545
Division of Polynomials; Rational Expressions
Find the quotient of (6x3 � 2x2).
6x3 � 2x2 � �62xx
3
2� � �(2)
((23))((xx))((xx))(x)
� � 3x
Find the quotient of (x3 � y3) � (x � y).
Factor the numerator; then look for common factors.
� x2 � xy � y2
Directions Divide.
1. 7x3 � x ________________________
2. (4x2 � x) � x ________________________
3. (15x4 � 3x3) � 3x ________________________
4. (18x5 � 6x2) � 2x2 ________________________
5. (x � y)5 � (x � y)3 ________________________
6. (6x � 4)6 � (6x � 4)3 ________________________
7. (x2 � 4xy � 4y2) � (x � 2y) ________________________
8. (4x2 � 20x � 25) � (2x � 5) ________________________
9. (9x2 � 24xy � 16y2) � (3x � 4y) ________________________
10. (x3 � y3) � (x � y) ________________________
11. (8x3 � 27) � (2x � 3) ________________________
12. (64x3 � y3) � (4x � y) ________________________
13. (16x2 � 4y2) � (4x � 2y) ________________________
14. (25 � 100y2) � (5 � 10y) ________________________
15. (8x3 � 8y3) � (4x2 � 4xy � 4y2) ________________________
(x � y)(x2 � xy � y2)���
(x � y)
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EXAMPLES
Name Date Period Workbook Activity
Chapter 5, Lesson 646
Long Division of Polynom