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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Chapter Review
      1. Key Terms
      2. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Chapter Review
      1. Key Terms
      2. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index

Be Prepared

8.1

6 y 6 y

8.2

2 x 1 3 x 2 2 x 1 3 x 2

8.3

n + 2 n 2 2 n + 4 n + 2 n 2 2 n + 4

8.4

4 25 4 25

8.5

49 9 49 9

8.6

2 x 7 x + 7 2 x 7 x + 7

8.7

10 n + 1 n 2 n + 1 10 n + 1 n 2 n + 1

8.8

5 2 p + q p 3 q 5 2 p + q p 3 q

8.9

y + 9 3 y + 9 3

8.10

8 x 8 x

8.12

5 a 3 a b 3 a + b 5 a 3 a b 3 a + b

8.13

37 30 37 30

8.14

8 x + 26 8 x + 26

8.15

3 x y 3 3 x y 3

8.16

12 4 n + 1 12 4 n + 1

8.17

2 3 2 3

8.18

1 54 1 54

8.19

x = 1 x = 1

8.20

n = 9 , n = 4 n = 9 , n = 4

8.21

y = 10 5 x 2 y = 10 5 x 2

8.22

n = 90 n = 90

8.23

7 feet 7 feet

8.24

28 mph 28 mph

8.25

x = 10 7 x = 10 7

8.26

t = 5 2 , t = 2 3 t = 5 2 , t = 2 3

8.27

1 8 1 8

8.28

n = 2.25 n = 2.25

8.29

500 500

Try It

8.1

x=0x=0 n=13n=13 a=−1,a=−3a=−1,a=−3

8.2

q=0q=0 y=23y=23 m=2,m=−3m=2,m=−3

8.3

−2−2 2929 1313

8.4

4343 66 −1−1

8.5

1212 1313 5

8.6

2323 4545 1212

8.7

−4−4 00 4949

8.8

00 316316 316316

8.9

5 9 . 5 9 .

8.10

7 9 7 9

8.11

x 3 y x 3 y

8.12

8 x y 8 x y

8.13

3 2 3 2

8.14

7 5 7 5

8.15

x + 1 x 1 x + 1 x 1

8.16

x 5 x 1 x 5 x 1

8.17

x + 3 x + 2 x + 3 x + 2

8.18

x + 1 x 7 x + 1 x 7

8.19

y 2 + 1 y + 2 y 2 + 1 y + 2

8.20

p 2 + 2 p + 5 p 2 + 2 p + 5

8.21

n 2 ( n + 1 ) n 2 ( n + 1 )

8.22

x 2 ( x + 2 ) x 2 ( x + 2 )

8.23

2 ( x 3 ) 3 ( x + 3 ) 2 ( x 3 ) 3 ( x + 3 )

8.24

5 ( y 1 ) 2 ( y + 5 ) 5 ( y 1 ) 2 ( y + 5 )

8.25

p 2 + 4 p + 16 p + 4 p 2 + 4 p + 16 p + 4

8.26

x 2 2 x + 4 x 2 x 2 2 x + 4 x 2

8.27

−1 −1

8.28

−1 −1

8.29

2 y + 5 . 2 y + 5 .

8.30

3 9 + y 3 9 + y

8.31

x + 1 x + 5 x + 1 x + 5

8.32

x + 2 x + 1 x + 2 x + 1

8.33

3 4 3 4

8.34

1 1

8.35

5 p 2 2 q 5 p 2 2 q

8.36

12 y 3 7 12 y 3 7

8.37

x 2 2 ( x + 3 ) x 2 2 ( x + 3 )

8.38

3 ( x 6 ) x + 5 3 ( x 6 ) x + 5

8.39

x + 5 x x + 5 x

8.40

x 4 x + 3 x 4 x + 3

8.41

6 ( x + 3 ) x + 2 6 ( x + 3 ) x + 2

8.42

v 3 v 3

8.43

1 1

8.44

1

8.45

1 c 3 1 c 3

8.46

1 2 + d 1 2 + d

8.47

( m 2 ) 4 ( m 8 ) ( m 2 ) 4 ( m 8 )

8.48

n ( n 2 ) n 1 n ( n 2 ) n 1

8.49

( a 3 ) ( a + 5 ) ( a 5 ) ( a 5 ) ( a 3 ) ( a + 5 ) ( a 5 ) ( a 5 )

8.50

( b + 2 ) ( b 1 ) ( 1 + b ) ( b + 4 ) ( b + 2 ) ( b 1 ) ( 1 + b ) ( b + 4 )

8.51

2 ( x 2 + 2 x + 4 ) ( x + 2 ) ( x 2 2 x + 4 ) 2 ( x 2 + 2 x + 4 ) ( x + 2 ) ( x 2 2 x + 4 )

8.52

2 z ( z 2 + z + 1 ) ( z + 1 ) ( z 2 z + 1 ) 2 z ( z 2 + z + 1 ) ( z + 1 ) ( z 2 z + 1 )

8.53

x 8 2 ( x + 1 ) x 8 2 ( x + 1 )

8.54

y 2 3 y 2 ( y 4 ) y 2 3 y 2 ( y 4 )

8.55

x + 2 4 x + 2 4

8.56

2 y + 5 2 y + 5

8.57

2 ( m + 1 ) ( m + 2 ) 3 ( m + 4 ) ( m 3 ) 2 ( m + 1 ) ( m + 2 ) 3 ( m + 4 ) ( m 3 )

8.58

( n + 5 ) ( n + 9 ) 2 ( n + 6 ) ( 2 n + 3 ) ( n + 5 ) ( n + 9 ) 2 ( n + 6 ) ( 2 n + 3 )

8.59

3 4 3 4

8.60

2 5 2 5

8.61

5 x + 2 2 x + 3 . 5 x + 2 2 x + 3 .

8.62

x + 1 x 2 x + 1 x 2

8.63

x + 2 x + 2

8.64

x + 3 x + 3

8.65

x 3 x 3

8.66

2 x + 5 2 x + 5

8.67

n + 3 n + 3

8.68

y 8 y 8

8.69

x 11 x 2 x 11 x 2

8.70

x 3 x + 9 x 3 x + 9

8.71

3 3

8.72

y + 3 y + 3

8.73

y + 3 y + 2 y + 3 y + 2

8.74

3 n 2 n 1 3 n 2 n 1

8.75

( x 4 ) ( x + 4 ) ( x + 3 ) ( x 4 ) ( x + 4 ) ( x + 3 )

8.76

( x + 3 ) ( x + 6 ) ( x + 5 ) ( x + 3 ) ( x + 6 ) ( x + 5 )

8.77

2 x + 8 ( x 4 ) ( x + 3 ) ( x + 4 ) , 2 x + 8 ( x 4 ) ( x + 3 ) ( x + 4 ) ,
x + 3 ( x 4 ) ( x + 3 ) ( x + 4 ) x + 3 ( x 4 ) ( x + 3 ) ( x + 4 )

8.78

x 2 + 6 x ( x + 3 ) ( x + 5 ) ( x + 6 ) , x 2 + 6 x ( x + 3 ) ( x + 5 ) ( x + 6 ) ,
5 x + 25 ( x + 3 ) ( x + 5 ) ( x + 6 ) 5 x + 25 ( x + 3 ) ( x + 5 ) ( x + 6 )

8.79

19 20 19 20

8.80

33 40 33 40

8.81

4 b + 25 a 30 a 2 b 2 4 b + 25 a 30 a 2 b 2

8.82

5 d 2 + 6 16 c d 2 5 d 2 + 6 16 c d 2

8.83

7 x 4 ( x + 3 ) ( x 2 ) 7 x 4 ( x + 3 ) ( x 2 )

8.84

7 m + 25 ( m + 3 ) ( m + 4 ) 7 m + 25 ( m + 3 ) ( m + 4 )

8.85

x ( 5 x + 7 y ) y ( x y ) ( x + y ) x ( 5 x + 7 y ) y ( x y ) ( x + y )

8.86

7 m + 15 2 ( m + 3 ) ( m + 1 ) 7 m + 15 2 ( m + 3 ) ( m + 1 )

8.87

5 m 2 9 m + 2 ( m 2 ) ( m + 1 ) ( m + 2 ) 5 m 2 9 m + 2 ( m 2 ) ( m + 1 ) ( m + 2 )

8.88

2 ( n 2 + 6 n 15 ) ( n + 2 ) ( n 5 ) ( n + 3 ) 2 ( n 2 + 6 n 15 ) ( n + 2 ) ( n 5 ) ( n + 3 )

8.89

−7 y + 8 ( y + 4 ) ( y 5 ) −7 y + 8 ( y + 4 ) ( y 5 )

8.90

4 z + 9 ( z + 2 ) ( z + 3 ) 4 z + 9 ( z + 2 ) ( z + 3 )

8.91

1 x 2 1 x 2

8.92

−3 z 3 −3 z 3

8.93

5 x + 1 x 6 x + 1 5 x + 1 x 6 x + 1

8.94

y + 3 y + 4 y + 3 y + 4

8.95

x + 22 x 7 x + 22 x 7

8.96

−2 ( 3 y 4 ) 2 y 1 −2 ( 3 y 4 ) 2 y 1

8.97

v + 3 v + 1 v + 3 v + 1

8.98

3 w w + 7 3 w w + 7

8.99

2 3 ( x 1 ) 2 3 ( x 1 )

8.100

1 2 ( x 3 ) 1 2 ( x 3 )

8.101

14 11 14 11

8.102

10 23 10 23

8.103

y + x y x y + x y x

8.104

a b b a a b b a

8.105

b b + 2 b 5 3 b 5 b b + 2 b 5 3 b 5

8.106

3 c + 3 3 c + 3

8.107

7 3 7 3

8.108

10 3 10 3

8.109

b + a a 2 + b 2 b + a a 2 + b 2

8.110

y x x y y x x y

8.111

3 x 6 5 x + 7 3 x 6 5 x + 7

8.112

x + 21 6 x 43 x + 21 6 x 43

8.113

3 5 x + 22 3 5 x + 22

8.114

6 y + 34 3 y 6 y + 34 3 y

8.115

x x + 4 x x + 4

8.116

x ( x + 1 ) 3 ( x 1 ) x ( x + 1 ) 3 ( x 1 )

8.117

15 7 15 7

8.118

15 13 15 13

8.119

5 , −3 5 , −3

8.120

6 , −2 6 , −2

8.121

−2 −2

8.122

−2 −2

8.123

2 3 2 3

8.124

2 2

8.125

−1 , −2 −1 , −2

8.126

−2 , −3 −2 , −3

8.127

no solution

8.128

y = 5 y = 5

8.129

−2 −2

8.130

−3 −3

8.131

3 3

8.132

7 7

8.133

no solution

8.134

no solution

8.135

L = A W L = A W

8.136

A = F M A = F M

8.137

x = 3 y 8 2 x = 3 y 8 2

8.138

y = x 1 + x y = x 1 + x

8.139

a = b c b 1 a = b c b 1

8.140

y = 3 x 6 + x y = 3 x 6 + x

8.141

77 77

8.142

104 104

8.143

65 65

8.144

24 24

8.145

33 33

8.146

14 14

8.147

42 42

8.148

6 6

8.149

12 ml 12 ml

8.150

180 mg 180 mg

8.151

464 calories 464 calories

8.152

5 pieces 5 pieces

8.153

590.4 Euros 590.4 Euros

8.154

56,460 yen 56,460 yen

8.156

22.5

8.157

150 miles

8.158

350 miles

8.159

40 feet

8.160

60 feet

8.161

15 mph

8.162

17 mph 17 mph

8.163

5 mph uphill and 10 mph downhill

8.164

50 mph 50 mph

8.165

15 mph 15 mph

8.166

6 mph 6 mph

8.167

2 hours and 24 minutes 2 hours and 24 minutes

8.168

2 hours and 6 minutes 2 hours and 6 minutes

8.169

16.25 hours

8.170

12 hours

8.171

y = 3 10 x y = 3 10 x

8.172

y = 3 x y = 3 x

8.173

c=4.8tc=4.8t 432 calories

8.174

d=50td=50t 250 miles

8.175

m=55hm=55h 220 miles

8.176

w=6vw=6v 78 pounds

8.177

d=16t2d=16t2 256 feet

8.178

A=3.14r2A=3.14r2 254.34 square inches

8.179

p = 360 q p = 360 q

8.180

y = 16 x y = 16 x

8.181

v=40,000av=40,000a $8,000

8.182

t=1000rt=1000r 2 hours

8.183

h=130th=130t 123123 hours

8.184

F=48LF=48L 9.6 pounds

Section 8.1 Exercises

1.

z=0z=0 p=56p=56 n=−4,n=2n=−4,n=2

3.

y=0y=0 x=12x=12 u=−4,u=7u=−4,u=7

5.

00 44 11

7.

33 5252 1515

9.

−6−6 203203 00

11.

−1−1 310310 00

13.

00 3434 154154

15.

00 3535 71207120

17.

1 13 1 13

19.

8 9 8 9

21.

b 2 a b 2 a

23.

2 m 2 3 n 2 m 2 3 n

25.

3 4 3 4

27.

3 5 3 5

29.

7 5 7 5

31.

12 5 12 5

33.

a + 3 a 4 a + 3 a 4

35.

y + 4 y 5 y + 4 y 5

37.

x 5 x 3 x 5 x 3

39.

y + 1 y + 3 y + 1 y + 3

41.

y 2 + 1 y + 1 y 2 + 1 y + 1

43.

x 2 x 2

45.

a ( a + 5 ) 2 ( a + 3 ) ( a 2 ) a ( a + 5 ) 2 ( a + 3 ) ( a 2 )

47.

c 2 ( c 5 ) c 2 ( c 5 )

49.

3 ( m + 5 ) 4 ( m 5 ) 3 ( m + 5 ) 4 ( m 5 )

51.

5 ( r 1 ) r 7 5 ( r 1 ) r 7

53.

t 2 + 3 t + 9 t + 3 t 2 + 3 t + 9 t + 3

55.

w 2 6 w + 36 w 6 w 2 6 w + 36 w 6

57.

−1 −1

59.

−1 −1

61.

2 x + 6 2 x + 6

63.

4 8 + v 4 8 + v

65.

( y 8 ) 3 + y ( y 8 ) 3 + y

67.

a + 4 9 + a a + 4 9 + a

69.

16.6%

71.

Answers will vary, but all should reference setting the denominator function to zero.

Section 8.2 Exercises

73.

3 10 3 10

75.

6 25 6 25

77.

x 3 8 y x 3 8 y

79.

8 a 4 3 b 2 8 a 4 3 b 2

81.

p ( p 4 ) 2 ( p 9 ) p ( p 4 ) 2 ( p 9 )

83.

r + 5 2 r ( r + 2 ) r + 5 2 r ( r + 2 )

85.

x 7 4 ( x + 3 ) x 7 4 ( x + 3 )

87.

z + 3 z ( z + 1 ) z + 3 z ( z + 1 )

89.

4 ( b + 9 ) 3 ( b + 7 ) 4 ( b + 9 ) 3 ( b + 7 )

91.

−7 −7

93.

1 1

95.

1 1

97.

6 t t + 3 t 5 6 t t + 3 t 5

99.

1 10 w 1 10 w

101.

3 y 2 ( y + 6 ) ( y + 7 ) ( y 7 ) ( y 2 + 6 ) 3 y 2 ( y + 6 ) ( y + 7 ) ( y 7 ) ( y 2 + 6 )

103.

a ( a 5 ) a 6 a ( a 5 ) a 6

105.

( c + 2 ) ( c + 2 ) ( c 2 ) ( c 3 ) ( c + 2 ) ( c + 2 ) ( c 2 ) ( c 3 )

107.

( m 2 ) ( m 3 ) ( 3 + m ) ( m + 4 ) ( m 2 ) ( m 3 ) ( 3 + m ) ( m + 4 )

109.

3 s s + 4 3 s s + 4

111.

4 ( p 2 p q + q 2 ) ( p q ) ( p 2 + p q + q 2 ) 4 ( p 2 p q + q 2 ) ( p q ) ( p 2 + p q + q 2 )

113.

t + 3 2 t ( t 3 ) t + 3 2 t ( t 3 )

115.

y + 3 z 2 y ( 2 y 1 ) y + 3 z 2 y ( 2 y 1 )

117.

2 a 7 5 2 a 7 5

119.

3 ( 3 c 5 ) 3 ( 3 c 5 )

121.

4 ( m + 8 ) ( m + 7 ) 3 ( m 4 ) ( m + 2 ) 4 ( m + 8 ) ( m + 7 ) 3 ( m 4 ) ( m + 2 )

123.

( 4 p + 1 ) ( p 4 ) 3 p ( p + 9 ) ( p 1 ) ( 4 p + 1 ) ( p 4 ) 3 p ( p + 9 ) ( p 1 )

125.

w(w1)(w+m)(w+m1)w(w1)(w+m)(w+m1)
221221

127.

Answers will vary.

Section 8.3 Exercises

129.

3 5 3 5

131.

3 4 3 4

133.

3 a + 1 a b 3 a + 1 a b

135.

d + 5 d + 8 d + 5 d + 8

137.

p + 8 p + 8

139.

r + 8 r + 8

141.

8 t 8 t

143.

2 w w 4 2 w w 4

145.

y 8 y 8

147.

3 a + 7 3 a + 7

149.

c + 2 c + 2

151.

m 2 2 m 2 2

153.

p + 3 p + 5 p + 3 p + 5

155.

r + 9 r + 7 r + 9 r + 7

157.

4 4

159.

x + 2 x + 2

161.

z + 4 z 5 z + 4 z 5

163.

4 b 3 b 7 4 b 3 b 7

165.

32 ( r + 1 ) r ( r + 4 ) 32 ( r + 1 ) r ( r + 4 )

Section 8.4 Exercises

169.

( x 4 ) ( x + 2 ) ( x + 3 ) ( x 4 ) ( x + 2 ) ( x + 3 )

171.

( z 2 ) ( z + 4 ) ( z + 2 ) ( z 2 ) ( z + 4 ) ( z + 2 )

173.

( b + 3 ) ( b + 3 ) ( b 5 ) ( b + 3 ) ( b + 3 ) ( b 5 )

175.

( 3 d 1 ) ( d + 5 ) ( d 6 ) ( 3 d 1 ) ( d + 5 ) ( d 6 )

177.

5 x + 15 ( x 4 ) ( x + 2 ) ( x + 3 ) , 5 x + 15 ( x 4 ) ( x + 2 ) ( x + 3 ) ,
2 x 2 + 4 x ( x 4 ) ( x + 2 ) ( x + 3 ) 2 x 2 + 4 x ( x 4 ) ( x + 2 ) ( x + 3 )

179.

9 z + 18 ( z 2 ) ( z + 4 ) ( z + 2 ) , 9 z + 18 ( z 2 ) ( z + 4 ) ( z + 2 ) ,
4 z 2 + 16 z ( z 2 ) ( z + 4 ) ( z + 2 ) 4 z 2 + 16 z ( z 2 ) ( z + 4 ) ( z + 2 )

181.

4 b 20 ( b + 3 ) ( b + 3 ) ( b 5 ) , 4 b 20 ( b + 3 ) ( b + 3 ) ( b 5 ) ,
2 b 2 + 6 b ( b + 3 ) ( b + 3 ) ( b 5 ) 2 b 2 + 6 b ( b + 3 ) ( b + 3 ) ( b 5 )

183.

2 d 12 ( 3 d 1 ) ( d + 5 ) ( d 6 ) , 2 d 12 ( 3 d 1 ) ( d + 5 ) ( d 6 ) ,
5 d 2 + 25 d ( 3 d 1 ) ( d + 5 ) ( d 6 ) 5 d 2 + 25 d ( 3 d 1 ) ( d + 5 ) ( d 6 )

185.

37 72 37 72

187.

49 60 49 60

189.

21 y + 8 x 30 x 2 y 2 21 y + 8 x 30 x 2 y 2

191.

4 m n + 7 8 m 2 n 4 m n + 7 8 m 2 n

193.

5 r 7 ( r + 4 ) ( r 5 ) 5 r 7 ( r + 4 ) ( r 5 )

195.

14 t 10 ( t + 5 ) ( t 5 ) 14 t 10 ( t + 5 ) ( t 5 )

197.

11 w + 1 ( 3 w 2 ) ( w + 1 ) 11 w + 1 ( 3 w 2 ) ( w + 1 )

199.

2 y 2 + y + 9 ( y + 3 ) ( y 1 ) 2 y 2 + y + 9 ( y + 3 ) ( y 1 )

201.

b ( 5 b + 10 + 2 a 2 ) a 2 ( b 2 ) ( b + 2 ) b ( 5 b + 10 + 2 a 2 ) a 2 ( b 2 ) ( b + 2 )

203.

2 m 2 + 23 m 3 ( m 1 ) ( m + 4 ) 2 m 2 + 23 m 3 ( m 1 ) ( m + 4 )

205.

4 n 2 9 n + 6 ( n 3 ) ( n + 6 ) ( n + 2 ) 4 n 2 9 n + 6 ( n 3 ) ( n + 6 ) ( n + 2 )

207.

3 ( r 2 + 6 r + 18 ) ( r + 1 ) ( r + 6 ) ( r + 3 ) 3 ( r 2 + 6 r + 18 ) ( r + 1 ) ( r + 6 ) ( r + 3 )

209.

2 ( 7 t 6 ) ( t 6 ) ( t + 6 ) 2 ( 7 t 6 ) ( t 6 ) ( t + 6 )

211.

−4 ( 1 + w ) ( w + 4 ) ( w 2 ) −4 ( 1 + w ) ( w + 4 ) ( w 2 )

213.

y 2 + 2 y 29 ( y + 1 ) ( y + 7 ) y 2 + 2 y 29 ( y + 1 ) ( y + 7 )

215.

4 a 2 + 25 a 6 ( a + 3 ) ( a + 6 ) 4 a 2 + 25 a 6 ( a + 3 ) ( a + 6 )

217.

3 c 5 3 c 5

219.

−6 m 6 −6 m 6

221.

p + 2 p + 3 p + 2 p + 3

223.

3 r 2 3 r 2

225.

v 14 v + 3 v 14 v + 3

227.

4 ( 8 x + 1 ) 10 x 1 4 ( 8 x + 1 ) 10 x 1

229.

5 a 2 + 7 a 36 a ( a 2 ) 5 a 2 + 7 a 36 a ( a 2 )

231.

c 5 c + 2 c 5 c + 2

233.

3 a ( 6 a b ) b ( 3 a + b ) ( 3 a b ) 3 a ( 6 a b ) b ( 3 a + b ) ( 3 a b )

235.

3 d + 8 3 d + 8

237.

2 ( 2 m 2 + 7 m 1 ) ( m + 7 ) ( m 1 ) ( m + 3 ) 2 ( 2 m 2 + 7 m 1 ) ( m + 7 ) ( m 1 ) ( m + 3 )

239.

n + 1 n + 8 n + 3 n 2 n + 1 n + 8 n + 3 n 2

241.

42 q + 25 90 p q 42 q + 25 90 p q

243.

7 ( x + 2 ) ( x 2 ) ( x + 5 ) 7 ( x + 2 ) ( x 2 ) ( x + 5 )

245.

1 q + 4 1 q + 4

247.

2 4 z + 1 ( z 5 ) ( z + 1 ) 2 4 z + 1 ( z 5 ) ( z + 1 )

249.

3 ( d + 1 ) d + 2 3 ( d + 1 ) d + 2

251.

2t+3t(t+3)2t+3t(t+3) 13401340

253.

Answers may vary.

Section 8.5 Exercises

255.

a 4 2 a a 4 2 a

257.

1 2 ( c 2 ) 1 2 ( c 2 )

259.

12 13 12 13

261.

20 57 20 57

263.

n 2 + m m n 2 n 2 + m m n 2

265.

r t t r r t t r

267.

( x + 1 ) ( x 3 ) 2 ( x + 1 ) ( x 3 ) 2

269.

4 a + 1 4 a + 1

271.

11 8 11 8

273.

19 19

275.

c 2 + c c d 2 c 2 + c c d 2

277.

p q q p p q q p

279.

2 x 10 3 x + 16 2 x 10 3 x + 16

281.

3 z 19 3 z + 8 3 z 19 3 z + 8

283.

4 3 a 7 4 3 a 7

285.

2 c + 29 5 c 2 c + 29 5 c

287.

( 2 p 5 ) 5 ( 2 p 5 ) 5

289.

m ( m 5 ) 4 m 2 + m 95 m ( m 5 ) 4 m 2 + m 95

291.

13 24 13 24

293.

2 ( a 4 ) 2 ( a 4 )

295.

3 m n n m 3 m n n m

297.

( x 1 ) ( x 2 ) 6 ( x 1 ) ( x 2 ) 6

299.

R1R2R2+R1R1R2R2+R1 245245

301.

Answers will vary.

Section 8.6 Exercises

303.

10 10

305.

4 7 4 7

307.

40 21 40 21

309.

−9 −9

311.

−2 , 4 −2 , 4

313.

−5 , −4 −5 , −4

315.

−6 −6

317.

14 14

319.

−4 5 −4 5

321.

1 3 1 3

323.

2 , 1 2 , 1

325.

−5 , −1 −5 , −1

327.

no solution no solution

329.

no solution no solution

331.

−4 −4

333.

−8 −8

335.

2 2

337.

1 1

339.

no solution no solution

341.

no solution no solution

343.

r = C 2 π r = C 2 π

345.

h = v l w h = v l w

347.

w = 2 v + 7 w = 2 v + 7

349.

c = b + 3 + 2 a a c = b + 3 + 2 a a

351.

p = q 4 q 2 p = q 4 q 2

353.

w = 15 v 10 + v w = 15 v 10 + v

355.

n = 5 m + 23 4 n = 5 m + 23 4

357.

y = 20 x 12 x y = 20 x 12 x

359.

t = 3 r s r t = 3 r s r

361.

26112611 days

363.

Answers will vary.

Section 8.7 Exercises

365.

49 49

367.

7 7

369.

9 9

371.

−11 −11

373.

7 7

375.

0.6 0.6

377.

16 16

379.

40 40

381.

60 60

383.

30 30

385.

9 ml 9 ml

387.

325 mg 325 mg

389.

159 calories 159 calories

391.

5 oz 5 oz

393.

252.5 Canadian dollars 252.5 Canadian dollars

395.

0.80 Euros 0.80 Euros

397.

0.63 British pounds 0.63 British pounds

399.

3 cups 3 cups

401.

1.30 Canadian dollars 1.30 Canadian dollars

403.

17 tsp 17 tsp

405.

3434 cup

407.

12 12

409.

77 18 77 18

411.

950 miles

413.

680 miles

415.

2323 foot (8in)(8in)

417.

247.3 feet 247.3 feet

419.

114 beats per minute
no

421.

19 gallons
$58.71

423.

4 bags

425.

5 pounds

427.

Answers will vary.

Section 8.8 Exercises

429.

160 mph 160 mph

431.

29 mph 29 mph

433.

30 mph 30 mph

435.

20 mph 20 mph

437.

4 mph 4 mph

439.

60 mph 60 mph

441.

650 mph 650 mph

443.

50 mph 50 mph

445.

50 mph 50 mph

447.

2 hours 2 hours

449.

2 hours and 44 minutes 2 hours and 44 minutes

451.

12 hours 12 hours

453.

7 hours and 30 minutes 7 hours and 30 minutes

455.

2 hours and 55 minutes 2 hours and 55 minutes

457.

4 hours 4 hours

459.

3 mph

Section 8.9 Exercises

463.

y = 14 3 x y = 14 3 x

465.

v = 3 w v = 3 w

467.

p = 3.2 q p = 3.2 q

469.

a = 18 b a = 18 b

471.

P=10nP=10n $40$40

473.

a=4.5pa=4.5p 27 apples

475.

p=3.98gp=3.98g $59.70$59.70

477.

m=8vm=8v 16 liters16 liters

479.

d=5t2d=5t2 245 feet

481.

A=3.14r2A=3.14r2 50.24sq. in.50.24sq. in.

483.

y = 20 x y = 20 x

485.

v = 3 w v = 3 w

487.

g=92,400wg=92,400w 16.8 mpg

489.

t=1000rt=1000r 2.5 hours2.5 hours

491.

L=4,400fL=4,400f 440 cycles per second

493.

t=125pt=125p 50 tickets

495.

y = 5 3 x y = 5 3 x

497.

p = 30 q p = 30 q

499.

p = 5 q p = 5 q

501.

5 pounds 5 pounds

503.

3 inches 3 inches

505.

15.6 mpg 15.6 mpg

507.

267.3 feet 267.3 feet

509.

c=2.5mc=2.5m $55

511.

Answers will vary.

Review Exercises

513.

a 2 3 a 2 3

515.

y 0 y 0

517.

5 6 5 6

519.

7 2 7 2

521.

5 12 5 12

523.

14 14

525.

c + 1 c + 2 c + 1 c + 2

527.

7 5 + v 7 5 + v

529.

1 20 1 20

531.

3 b 3 b

533.

6 t ( t + 6 ) 2 6 t ( t + 6 ) 2

535.

−1 11 w −1 11 w

537.

5 c + 4 5 c + 4

539.

1 1

541.

p + 5 p + 5

543.

d 7 d 7

545.

q - 3 q + 5 q - 3 q + 5

547.

15 w + 2 6 w 1 15 w + 2 6 w 1

549.

3 b 2 + 19 b 16 b 7 b + 7 3 b 2 + 19 b 16 b 7 b + 7

551.

( m + 2 ) ( m 5 ) ( m + 4 ) ( m + 2 ) ( m 5 ) ( m + 4 )

553.

( 3 p + 1 ) ( p + 6 ) ( p + 8 ) ( 3 p + 1 ) ( p + 6 ) ( p + 8 )

555.

6 n + 12 ( n 2 ) ( n 2 ) ( n + 2 ) , 6 n + 12 ( n 2 ) ( n 2 ) ( n + 2 ) ,
2 n 2 4 n ( n 2 ) ( n 2 ) ( n + 2 ) 2 n 2 4 n ( n 2 ) ( n 2 ) ( n + 2 )

557.

19 15 19 15

559.

11 c 12 ( c 2 ) ( c + 3 ) 11 c 12 ( c 2 ) ( c + 3 )

561.

5 x 2 + 26 x ( x + 4 ) ( x + 4 ) ( x + 6 ) 5 x 2 + 26 x ( x + 4 ) ( x + 4 ) ( x + 6 )

563.

2 ( v 2 + 10 v 2 ) ( v + 2 ) ( v + 8 ) 2 ( v 2 + 10 v 2 ) ( v + 2 ) ( v + 8 )

565.

2 m 7 m + 2 2 m 7 m + 2

567.

4 d 8 4 d 8

569.

a 2 2 a a 2 2 a

571.

( x + 2 ) ( x 5 ) 2 ( x + 2 ) ( x 5 ) 2

573.

2 3 q 11 q + 4 5 ( q 4 ) 2 3 q 11 q + 4 5 ( q 4 )

575.

z 5 21 z + 21 z 5 21 z + 21

577.

6 7 6 7

579.

3 2 3 2

581.

no solution no solution

583.

l = V h w l = V h w

585.

z = y + 5 + 7 x x z = y + 5 + 7 x x

587.

12 5 12 5

589.

15 15

591.

1126 calories 1126 calories

593.

b = 9 ; x = 2 1 3 b = 9 ; x = 2 1 3

595.

23 feet

597.

45 mph 45 mph

599.

16 mph 16 mph

601.

4 5 hour 4 5 hour

603.

12 days 12 days

605.

7 7

607.

36 36

609.

$ 9 $ 9

611.

9 tickets 9 tickets

Practice Test

613.

a 2 b a 2 b

615.

x + 3 3 x x + 3 3 x

617.

4 + 5 q p q 4 + 5 q p q

619.

19 6 19 6

621.

14 11 14 11

623.

1 2 1 2

625.

4

627.

60

629.

125 mg 125 mg

631.

34 mph 34 mph

633.

1 5 9 hours 1 5 9 hours

635.

$ 74.70 $ 74.70

637.

64 miles

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