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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

6.1

11 x 11 x

6.2

3 n + 9 3 n + 9

6.3

a a a a a a a a a a

6.4

3 4 · 3 4 3 4 · 3 4

6.5

8 8

6.6

2 x + 6 2 x + 6

6.7

x 2 + 16 x + 63 x 2 + 16 x + 63

6.8

8181 8181 8181

6.9

1 3 1 3

6.10

32 m 15 32 m 15

6.11

x y x y

6.12

3 + x d 3 + x d

6.13

6 y 2 6 y 2

6.14

11 a 2 + 7 a + 5 11 a 2 + 7 a + 5

6.15

Ten thousands

6.16

Twelve ten thousandths

6.17

8 8

Try It

6.1

monomial polynomial trinomial binomial monomial

6.2

binomial trinomial monomial polynomial monomial

6.3

11 44 1212 3 0

6.4

00 55 11 2 3

6.5

21 q 2 21 q 2

6.6

−7 c 2 −7 c 2

6.7

13 m 13 m

6.8

−10 z 3 −10 z 3

6.9

5 y 2 + 3 z 2 5 y 2 + 3 z 2

6.10

−4 m 2 + n 2 −4 m 2 + n 2

6.11

There are no like terms to combine.

6.12

There are no like terms to combine.

6.13

8 x 2 11 x + 8 8 x 2 11 x + 8

6.14

17 y 2 + 14 y + 1 17 y 2 + 14 y + 1

6.15

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

6.16

6 b 2 + 3 6 b 2 + 3

6.17

2 z 2 + 12 z 2 2 z 2 + 12 z 2

6.18

5 x 2 + 14 x + 7 5 x 2 + 14 x + 7

6.19

5 x 2 5 x y + 5 y 2 5 x 2 5 x y + 5 y 2

6.20

7 x 2 6 x y 2 y 2 7 x 2 6 x y 2 y 2

6.21

5 a b + 7 b 2 5 a b + 7 b 2

6.22

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

6.23

x 3 y 3 x 3 y 3

6.24

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

6.25

1818 5050 −15−15

6.26

1818 −4−4 1414

6.27

250 250

6.28

106 106

6.29

$576

6.30

$750

6.31

216 1515 949949 0.1849

6.32

3232 21 81258125 0.0475240.047524

6.33

8181 −81−81

6.34

169169 −169−169

6.35

b 17 b 17

6.36

x 16 x 16

6.37

5656 418418

6.38

714714 10111011

6.39

p6p6 y43y43

6.40

z8z8 b49b49

6.41

x 18 x 18

6.42

b 19 b 19

6.43

b35b35 512512

6.44

z54z54 349349

6.45

144y2144y2 32w5x532w5x5

6.46

125w3x3125w3x3 −27y3−27y3

6.47

a48a48 −8c12d6−8c12d6

6.48

81x24y2881x24y28 q29q29

6.49

75n1275n12 81c24d3081c24d30

6.50

256a22b24256a22b24 40x1040x10

6.51

−35 y 11 −35 y 11

6.52

54 b 9 54 b 9

6.53

6 a 5 b 6 6 a 5 b 6

6.54

8 r 11 s 8 8 r 11 s 8

6.55

5 x + 35 5 x + 35

6.56

3 y + 39 3 y + 39

6.57

x 2 7 x x 2 7 x

6.58

d 2 11 d d 2 11 d

6.59

5 x 2 + 20 x y 5 x 2 + 20 x y

6.60

12 p 2 + 2 p r 12 p 2 + 2 p r

6.61

−15 y 3 24 y 2 + 21 y −15 y 3 24 y 2 + 21 y

6.62

8 x 4 12 x 3 + 20 x 2 8 x 4 12 x 3 + 20 x 2

6.63

12 x 3 20 x 2 + 12 x 12 x 3 20 x 2 + 12 x

6.64

−18 a 5 + 12 a 4 36 a 3 −18 a 5 + 12 a 4 36 a 3

6.65

x p + 8 p x p + 8 p

6.66

a p + 4 p a p + 4 p

6.67

x 2 + 17 x + 72 x 2 + 17 x + 72

6.68

20 x 2 + 51 x + 27 20 x 2 + 51 x + 27

6.69

12 b 2 + 38 b + 30 12 b 2 + 38 b + 30

6.70

a 2 + 17 a + 70 a 2 + 17 a + 70

6.71

30 y 2 3 y 6 30 y 2 3 y 6

6.72

15 c 2 + 14 c 8 15 c 2 + 14 c 8

6.73

a 2 a b + 7 a 7 b a 2 a b + 7 a 7 b

6.74

x 2 x y + 5 x 5 y x 2 x y + 5 x 5 y

6.75

x 2 + 14 x + 48 x 2 + 14 x + 48

6.76

y 2 + 20 y + 51 y 2 + 20 y + 51

6.77

x 2 2 x 35 x 2 2 x 35

6.78

b 2 + 3 b 18 b 2 + 3 b 18

6.79

15 x 2 + 29 x 14 15 x 2 + 29 x 14

6.80

16 y 2 20 y 50 16 y 2 20 y 50

6.81

10 c 2 60 c c d + 6 d 10 c 2 60 c c d + 6 d

6.82

14 x 2 35 x 2 x y + 5 y 14 x 2 35 x 2 x y + 5 y

6.83

x 3 8 x 2 + 6 x 48 x 3 8 x 2 + 6 x 48

6.84

y 3 9 y 2 + 7 y 63 y 3 9 y 2 + 7 y 63

6.85

8 a 2 b 2 + 12 a b 20 8 a 2 b 2 + 12 a b 20

6.86

8 x 2 y 2 + 2 x y 15 8 x 2 y 2 + 2 x y 15

6.87

15 m 2 51 m + 42 15 m 2 51 m + 42

6.88

42 b 2 53 b + 15 42 b 2 53 b + 15

6.89

y 3 8 y 2 + 17 y 6 y 3 8 y 2 + 17 y 6

6.90

2 x 3 + 5 x 2 7 x + 20 2 x 3 + 5 x 2 7 x + 20

6.91

y 3 8 y 2 + 17 y 6 y 3 8 y 2 + 17 y 6

6.92

2 x 3 + 5 x 2 7 x + 20 2 x 3 + 5 x 2 7 x + 20

6.93

x 2 + 18 x + 81 x 2 + 18 x + 81

6.94

y 2 + 22 y + 121 y 2 + 22 y + 121

6.95

x 2 18 x + 81 x 2 18 x + 81

6.96

p 2 26 p + 169 p 2 26 p + 169

6.97

36 x 2 + 36 x + 9 36 x 2 + 36 x + 9

6.98

16 x 2 + 72 x + 81 16 x 2 + 72 x + 81

6.99

4 c 2 4 c d + d 2 4 c 2 4 c d + d 2

6.100

16 x 2 40 x y + 25 y 2 16 x 2 40 x y + 25 y 2

6.101

4 x 4 + 4 x 2 + 1 4 x 4 + 4 x 2 + 1

6.102

9 y 6 + 12 y 3 + 4 9 y 6 + 12 y 3 + 4

6.103

x 2 25 x 2 25

6.104

w 2 9 w 2 9

6.105

36 x 2 25 36 x 2 25

6.106

4 x 2 49 4 x 2 49

6.107

49 16 x 2 49 16 x 2

6.108

81 4 y 2 81 4 y 2

6.109

16 p 2 49 q 2 16 p 2 49 q 2

6.110

9 x 2 y 2 9 x 2 y 2

6.111

x 2 y 2 36 x 2 y 2 36

6.112

a 2 b 2 81 a 2 b 2 81

6.113

9 x 4 16 y 6 9 x 4 16 y 6

6.114

4 m 4 25 n 6 4 m 4 25 n 6

6.115

FOIL; 18b2+77b1818b2+77b18 Binomial Squares; 81p272p+1681p272p+16 Binomial Squares; 49y2+14y+149y2+14y+1 Product of Conjugates; 16r2916r29

6.116

Binomial Squares; 36x2+84x+4936x2+84x+49 Product of Conjugates; 9x2169x216 FOIL; 10x229x+1010x229x+10 Binomial Squares; 36n212n+136n212n+1

6.117

x5x5 6969

6.118

y6y6 108108

6.119

1x41x4 1121511215

6.120

1m81m8 19111911

6.121

b8b8 1z61z6

6.122

1p81p8 w4w4

6.123

1 1

6.124

1 1

6.125

11 11

6.126

11 11

6.127

25642564 p410,000p410,000 m7n7m7n7

6.128

127127 −8q3−8q3 w4x4w4x4

6.129

m 13 m 13

6.130

k 5 k 5

6.133

r 8 r 8

6.134

v 6 v 6

6.135

a 12 b 8 a 12 b 8

6.136

q 21 r 15 q 21 r 15

6.137

49 x 6 81 y 2 49 x 6 81 y 2

6.138

9 x 8 49 y 2 9 x 8 49 y 2

6.139

1 a 6 1 a 6

6.140

1 p 15 1 p 15

6.141

9 r 18 9 r 18

6.142

2 x 2 x

6.143

7 y 6 7 y 6

6.144

6 z 6 6 z 6

6.145

9 a 5 b 9 a 5 b

6.146

−9 d c 4 −9 d c 4

6.147

2 a 6 3 b 2 2 a 6 3 b 2

6.148

3 q 6 5 p 8 3 q 6 5 p 8

6.149

4 y 2 7 x 4 4 y 2 7 x 4

6.150

5 8 m 5 n 3 5 8 m 5 n 3

6.151

2 a b 2 2 a b 2

6.152

−4 x y 5 −4 x y 5

6.153

2 z 2 + 6 2 z 2 + 6

6.154

2 z 2 3 2 z 2 3

6.155

9 b 2 11 b 9 b 2 11 b

6.156

5 y 2 11 y 5 y 2 11 y

6.157

−5 y 2 + 3 y −5 y 2 + 3 y

6.158

−7 b 2 + 3 b −7 b 2 + 3 b

6.159

15 d 4 + 6 d 2 15 d 4 + 6 d 2

6.160

36 p 4 8 p 2 36 p 4 8 p 2

6.161

−4 a + 2 b −4 a + 2 b

6.162

8 a 5 b + 6 a 3 b 2 8 a 5 b + 6 a 3 b 2

6.163

5 x y + 3 y 2 y 2 5 x y + 3 y 2 y 2

6.164

5 a 2 + 2 a 2 b 6 b 2 5 a 2 + 2 a 2 b 6 b 2

6.165

3 c + 1 3 2 c 3 c + 1 3 2 c

6.166

2 d 1 2 5 d 2 d 1 2 5 d

6.167

y + 7 y + 7

6.168

m + 5 m + 5

6.169

2 x + 5 2 x + 5

6.170

3 x + 2 3 x + 2

6.171

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

6.172

2 x 2 + 6 x 5 3 x + 1 2 x 2 + 6 x 5 3 x + 1

6.173

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

6.174

x 3 8 x 2 + 40 x 200 x 3 8 x 2 + 40 x 200

6.175

x 2 + 4 x + 16 x 2 + 4 x + 16

6.176

25 x 2 + 10 x + 4 25 x 2 + 10 x + 4

6.177

1818 11071107

6.178

1919 110,000110,000

6.179

p8p8 6464

6.180

q7q7 1616

6.181

81168116 n236m2n236m2

6.182

1252712527 16b4a416b4a4

6.183

125125 125125 25 −25−25

6.184

149149 149149 49 −49−49

6.185

22 118118

6.186

2 12561256

6.187

1y71y7 1z151z15

6.188

1p91p9 1q241q24

6.189

8p8p 18p18p 18p18p

6.190

111q111q 111q111q111q111q 11q11q

6.191

x4x4 1y51y5 1z91z9

6.192

a5a5 1b41b4 1c151c15

6.193

1 p 3 q 3 1 p 3 q 3

6.194

1 r 2 s 8 1 r 2 s 8

6.195

30 d 3 c 8 30 d 3 c 8

6.196

1 16 x 8 1 16 x 8

6.197

1 16 b 12 1 16 b 12

6.198

64 a 8 64 a 8

6.199

8 c 12 8 c 12

6.200

x 11 x 11

6.201

y 14 y 14

6.202

9.6 × 10 4 9.6 × 10 4

6.203

4.83 × 10 4 4.83 × 10 4

6.204

7.8 × 10 −3 7.8 × 10 −3

6.205

1.29 × 10 −2 1.29 × 10 −2

6.206

1,300

6.207

92,500

6.208

0.00012

6.209

0.075

6.210

0.06

6.211

0.009

6.212

400,000

6.213

20,000

Section 6.1 Exercises

1.

trinomial polynomial binomial monomial binomial

3.

binomial trinomial polynomial trinomial monomial

5.

2 4 1 3 0

7.

1 2 3 3 0

9.

12 x 2 12 x 2

11.

6 w 6 w

13.

−5 a −5 a

15.

40 x 40 x

17.

−22 b −22 b

19.

−10a + 5 b −10a + 5 b

21.

−4 a 2 + b 2 −4 a 2 + b 2

23.

x y 2 5 x 5 y 2 x y 2 5 x 5 y 2

25.

a 2 b 4 a 5 a b 2 a 2 b 4 a 5 a b 2

27.

12a + 8 b 12a + 8 b

29.

−4 a 3 b −4 a 3 b

31.

−17 x 6 −17 x 6

33.

11 y 2 + 4 y + 11 11 y 2 + 4 y + 11

35.

−3 x 2 + 17 x 1 −3 x 2 + 17 x 1

37.

11 x 2 5 x + 5 11 x 2 5 x + 5

39.

6 a 2 4 a 1 6 a 2 4 a 1

41.

2 m 2 7 m + 4 2 m 2 7 m + 4

43.

11 a + 3 11 a + 3

45.

12 s 2 16 s + 9 12 s 2 16 s + 9

47.

3 x 2 x + 4 3 x 2 x + 4

49.

w 2 + 3 w + 4 w 2 + 3 w + 4

51.

2 p 3 + p 2 + 9 p + 10 2 p 3 + p 2 + 9 p + 10

53.

8 a 3 + a 2 2 a + 12 8 a 3 + a 2 2 a + 12

55.

11 w 66 11 w 66

57.

12 c 45 12 c 45

59.

10 x 2 7 x y + 6 y 2 10 x 2 7 x y + 6 y 2

61.

10 m 2 + 3 m n 8 n 2 10 m 2 + 3 m n 8 n 2

63.

−3 a b + 3 b 2 −3 a b + 3 b 2

65.

4 u v + 2 v 2 4 u v + 2 v 2

67.

p 3 6 p 2 q + p q 2 + 4 q 3 p 3 6 p 2 q + p q 2 + 4 q 3

69.

x 3 + 2 x 2 y 5 x y 2 + y 3 x 3 + 2 x 2 y 5 x y 2 + y 3

71.

187 40 2

73.

−104 4 40

75.

11

77.

$10,800

79.

4

81.

$58

83.

149

85.

Answers will vary.

87.

Answers will vary.

Section 6.2 Exercises

89.

10,000 17 481481 0.125

91.

512 8 27642764
0.064

93.

64 −64−64

95.

4949 4949

97.

−0.0001−0.0001 0.0001

99.

x 6 x 6

101.

q 42 q 42

103.

316316 5555

105.

w6w6 u94u94

107.

y 9 y 9

109.

c 18 c 18

111.

n y + 2 n y + 2

113.

x p + q x p + q

115.

b14b14 316316

117.

x2yx2y 7ab7ab

119.

25x225x2 16a2b216a2b2

121.

−343n3−343n3 81x4y4z481x4y4z4

123.

w22w22 32x5y2032x5y20

125.

−1000q6p12−1000q6p12 n40n40

127.

48y448y4 25,000k2425,000k24

129.

432b5432b5 1200j161200j16

131.

128r8128r8 27x2927x29

133.

−18 y 11 −18 y 11

135.

72 u 7 72 u 7

137.

4 f 11 4 f 11

139.

36 a 5 b 7 36 a 5 b 7

141.

8 r 2 s 5 8 r 2 s 5

143.

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

145.

x 14 x 14

147.

a 36 a 36

149.

8 m 18 8 m 18

151.

1000 x 6 y 3 1000 x 6 y 3

153.

16 a 12 b 8 16 a 12 b 8

155.

8 27 x 6 y 3 8 27 x 6 y 3

157.

1024 a 10 1024 a 10

159.

25000 p 24 25000 p 24

161.

x 18 y 18 x 18 y 18

163.

144 m 8 n 22 144 m 8 n 22

165.

1,000,000 1,000,000

167.

$168.07

169.

Answers will vary.

171.

Answers will vary.

Section 6.3 Exercises

173.

4 w + 40 4 w + 40

175.

−3 a 21 −3 a 21

177.

2 x 14 2 x 14

179.

−3 k + 12 −3 k + 12

181.

q 2 + 5 q q 2 + 5 q

183.

b 2 9 b b 2 9 b

185.

x 2 + 10 x x 2 + 10 x

187.

24 r 2 + 6 r s 24 r 2 + 6 r s

189.

12 x 2 120 x 12 x 2 120 x

191.

−27 a 2 45 a −27 a 2 45 a

193.

3 p 2 + 30 p + 75 3 p 2 + 30 p + 75

195.

−8 x 3 16 x 2 + 120 x −8 x 3 16 x 2 + 120 x

197.

5 q 6 10 q 4 + 30 q 3 5 q 6 10 q 4 + 30 q 3

199.

−8 y 3 16 y 2 + 120 y −8 y 3 16 y 2 + 120 y

201.

5 q 5 10 q 4 + 30 q 3 5 q 5 10 q 4 + 30 q 3

203.

−12 z 4 48 z 3 + 4 z 2 −12 z 4 48 z 3 + 4 z 2

205.

2 m 2 9 m 2 m 2 9 m

207.

8 w 48 8 w 48

209.

4 x + 40 4 x + 40

211.

15 r 360 15 r 360

213.

−3 m 33 −3 m 33

215.

−8 z + 40 −8 z + 40

217.

u 2 + 5 u u 2 + 5 u

219.

n 3 3 n 2 n 3 3 n 2

221.

24 x 2 + 6 x y 24 x 2 + 6 x y

223.

55 p 2 25 p q 55 p 2 25 p q

225.

3 v 2 + 30 v + 75 3 v 2 + 30 v + 75

227.

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

229.

−8 y 3 16 y 2 + 120 y −8 y 3 16 y 2 + 120 y

231.

5 q 5 10 q 4 + 30 q 3 5 q 5 10 q 4 + 30 q 3

233.

−12 z 4 48 z 3 + 4 z 2 −12 z 4 48 z 3 + 4 z 2

235.

2 y 2 9 y 2 y 2 9 y

237.

w 2 + 12 w + 35 w 2 + 12 w + 35

239.

p 2 + 7 p 44 p 2 + 7 p 44

241.

x 2 + 11 x + 24 x 2 + 11 x + 24

243.

y 2 8 y + 12 y 2 8 y + 12

245.

w 2 + 3 w 28 w 2 + 3 w 28

247.

p 2 + 7 p 60 p 2 + 7 p 60

249.

6 p 2 + 11 p + 5 6 p 2 + 11 p + 5

251.

20 t 2 88 t 9 20 t 2 88 t 9

253.

15 x 2 3 x y 30 x + 6 y 15 x 2 3 x y 30 x + 6 y

255.

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

257.

4 z 2 24 z z y + 6 y 4 z 2 24 z z y + 6 y

259.

x 3 + 2 x 2 + 3 x + 6 x 3 + 2 x 2 + 3 x + 6

261.

x 4 + 3 x 2 40 x 4 + 3 x 2 40

263.

10 a 2 b 2 + 13 a b 3 10 a 2 b 2 + 13 a b 3

265.

24 p 2 q 2 42 p q + 15 24 p 2 q 2 42 p q + 15

267.

x 3 + 9 x 2 + 23 x + 15 x 3 + 9 x 2 + 23 x + 15

269.

4 y 3 + 33 y 2 + y 56 4 y 3 + 33 y 2 + y 56

271.

w 3 16 w 2 + 73 w 70 w 3 16 w 2 + 73 w 70

273.

3 q 3 11 q 2 19 q 5 3 q 3 11 q 2 19 q 5

275.

14 y 13 14 y 13

277.

−11 x 28 −11 x 28

279.

15 q 3 30 q 2 + 55 q 15 q 3 30 q 2 + 55 q

281.

s 2 + 2 s 63 s 2 + 2 s 63

283.

y 3 y 2 2 y y 3 y 2 2 y

285.

3 n 3 n 2 25 n + 28 3 n 3 n 2 25 n + 28

287.

49 p 2 100 49 p 2 100

289.

4 m 4 3 m 3 7 m 2 4 m 4 3 m 3 7 m 2

291.

25 a 2 + 70 a b + 49 b 2 25 a 2 + 70 a b + 49 b 2

293.

16 y 2 144 z 2 16 y 2 144 z 2

295.

306 306 Answers will vary.

297.

Answers will vary.

299.

Answers may vary.

301.

Answers may vary.

Section 6.4 Exercises

303.

q 2 + 24 q + 144 q 2 + 24 q + 144

305.

x 2 + 4 3 x + 4 9 x 2 + 4 3 x + 4 9

307.

y 2 12 y + 36 y 2 12 y + 36

309.

p 2 26 p + 169 p 2 26 p + 169

311.

16 a 2 + 80 a + 100 16 a 2 + 80 a + 100

313.

9 z 2 + 6 5 z + 1 25 9 z 2 + 6 5 z + 1 25

315.

4 y 2 12 y z + 9 z 2 4 y 2 12 y z + 9 z 2

317.

1 64 x 2 1 36 x y + 1 81 y 2 1 64 x 2 1 36 x y + 1 81 y 2

319.

25 u 4 + 90 u 2 + 81 25 u 4 + 90 u 2 + 81

321.

64 p 6 48 p 3 + 9 64 p 6 48 p 3 + 9

323.

c 2 25 c 2 25

325.

b 2 36 49 b 2 36 49

327.

64 j 2 16 64 j 2 16

329.

81 c 2 25 81 c 2 25

331.

169 q 2 169 q 2

333.

16 36 y 2 16 36 y 2

335.

49 w 2 100 x 2 49 w 2 100 x 2

337.

p 2 16 25 q 2 p 2 16 25 q 2

339.

x 2 y 2 81 x 2 y 2 81

341.

r 2 s 2 4 49 r 2 s 2 4 49

343.

36 m 6 16 n 10 36 m 6 16 n 10

345.

225 m 4 64 n 8 225 m 4 64 n 8

347.

4r2+48r+1444r2+48r+144 9p2649p264 7a248ab7b27a248ab7b2 k212k+36k212k+36

349.

x10y10x10y10 m616m3n+64n2m616m3n+64n2 81p2+144pq+64q281p2+144pq+64q2 r5+r2s2r3s3s5r5+r2s2r3s3s5

351.

4,225 4,225 Answers will vary.

353.

Answers will vary.

355.

Answers will vary.

Section 6.5 Exercises

357.

y10y10 714714

359.

u21u21 910910

361.

1t301t30 164164

363.

1x61x6 11001100

365.

1 1

367.

−1−1 −1−1

369.

1 6

371.

7 1

373.

−7−7 0

375.

425425 x481x481 a5b5a5b5

377.

x38y3x38y3 10,00081q410,00081q4

379.

p 7 p 7

381.

x 5 x 5

383.

1

385.

1 n 16 1 n 16

387.

q 18 q 18

389.

1 m 12 1 m 12

391.

a 3 b 18 a 3 b 18

393.

y 20 z 50 y 20 z 50

395.

27 m 15 125 n 3 27 m 15 125 n 3

397.

625 u 28 16 v 12 625 u 28 16 v 12

399.

j 9 j 9

401.

1 q 8 1 q 8

403.

64 k 6 64 k 6

405.

−4,000 −4,000

407.

7 v 8 7 v 8

409.

−6 u 8 −6 u 8

411.

3 x 3 y 12 3 x 3 y 12

413.

2 m 3 3 n 5 2 m 3 3 n 5

415.

−3 y 3 4 x 3 −3 y 3 4 x 3

417.

65 a 3 b 2 42 c 3 65 a 3 b 2 42 c 3

419.

−3 q 5 p 5 −3 q 5 p 5

421.

5 v 4 u 2 5 v 4 u 2

423.

18n1018n10 12n1012n10 45n2045n20 5

425.

q8q8 q15q15

427.

zz 1z1z

429.

6 y 6 6 y 6

431.

15 c 6 15 c 6

433.

3 x 2 3 x 2

435.

y z 2 y z 2

437.

10 3 10 3

439.

Answers will vary.

441.

Answers will vary.

Section 6.6 Exercises

443.

6 b + 15 6 b + 15

445.

6 x 2 2 x 6 x 2 2 x

447.

11 w 2 11 w 2

449.

4 x 2 + 3 x 4 x 2 + 3 x

451.

−5 b 2 + 3 b −5 b 2 + 3 b

453.

−17 m 4 24 m 3 −17 m 4 24 m 3

455.

103 z 5 12 z 2 103 z 5 12 z 2

457.

17 y 2 + 14 17 y 2 + 14

459.

−5 x 3 + 3 −5 x 3 + 3

461.

−6 y 2 + 3 y −6 y 2 + 3 y

463.

9 x 2 y 3 + 12 y 9 x 2 y 3 + 12 y

465.

7 c 10 c 2 d 5 c d 2 7 c 10 c 2 d 5 c d 2

467.

6 r 3 + 11 r 2 s 8 r s 3 6 r 3 + 11 r 2 s 8 r s 3

469.

4 q + 1 1 3 q 4 q + 1 1 3 q

471.

−5 y 3 + 1 4 y −5 y 3 + 1 4 y

473.

7 a 12 + 11 a 7 a 12 + 11 a

475.

d + 6 d + 6

477.

a 7 a 7

479.

x 7 x 7

481.

4 x + 3 4 x + 3

483.

p + 3 8 p + 8 p + 3 8 p + 8

485.

x + 7 + 5 x 5 x + 7 + 5 x 5

487.

2 n 2 6 n + 8 2 n 2 6 n + 8

489.

7 q 2 + 7 q + 2 7 q 2 + 7 q + 2

491.

m 2 10 m + 100 m 2 10 m + 100

493.

x 2 + 6 x + 36 x 2 + 6 x + 36

495.

25 y 2 + 20 x + 16 25 y 2 + 20 x + 16

497.

45

499.

Answers will vary.

Section 6.7 Exercises

501.

181181 11001100

503.

12561256 11001100

505.

c5c5 25

507.

t9t9 10000

509.

10091009 c3d38c3d38

511.

83438343 x3y627x3y627

513.

149149 149149 49 −49−49

515.

11251125 −125−125 −125−125 11251125

517.

2525 110110

519.

316316 11441144

521.

1b51b5 1k101k10

523.

1s81s8 1a901a90

525.

6r6r 16r16r 16r16r

527.

116q4116q4 2q42q4 2q42q4

529.

1s41s4 1q51q5 1y71y7

531.

1 y6y6 1y41y4

533.

1 x 1 x

535.

1 m 2 n 4 1 m 2 n 4

537.

1 p 5 q 7 1 p 5 q 7

539.

14 k 5 j 3 14 k 5 j 3

541.

40 n 3 m 40 n 3 m

543.

1 64 y 9 1 64 y 9

545.

4 p 10 4 p 10

547.

n 7 n 7

549.

y 5 y 5

551.

3.4 × 10 5 3.4 × 10 5

553.

1.29 × 10 6 1.29 × 10 6

555.

4.1 × 10 −2 4.1 × 10 −2

557.

1.03 × 10 −6 1.03 × 10 −6

559.

830

561.

16,000,000,000

563.

0.038

565.

0.0000193

567.

0.02

569.

0.0000056 0.0000056

571.

500,000,000

573.

20,000,000

575.

6.85×1096.85×109.

577.

5.7 × 10 −9 5.7 × 10 −9

579.

15,000,000,000,000

581.

0.00001

583.

1.545 × 10 8 1.545 × 10 8

585.

1.86×10131.86×1013 3×1083×108 6.2×1046.2×104

587.

answers will vary

Review Exercises

589.

binomial monomial trinomial trinomial other polynomial

591.

3 4 2 4 0

593.

5 k 5 k

595.

−27 c −27 c

597.

7 n 2 7 n 2

599.

13a + b 13a + b

601.

13 p 2 5 p 1 13 p 2 5 p 1

603.

7 y 2 9 y + 4 7 y 2 9 y + 4

605.

5 a 3 + a 2 + 6 a + 2 5 a 3 + a 2 + 6 a + 2

607.

−26−26 10 22

609.

12,000

611.

17

613.

0.125

615.

−64 −64

617.

p 31 p 31

619.

8 6 8 6

621.

y c + 3 y c + 3

623.

5 6 5 6

625.

3 r s 3 r s

627.

−125 y 3 −125 y 3

629.

1000 x 3 y 3 z 3 1000 x 3 y 3 z 3

631.

64 a 9 b 6 64 a 9 b 6

633.

144 q 14 144 q 14

635.

8 125 m 6 n 3 8 125 m 6 n 3

637.

144 n 8 144 n 8

639.

15 a 2 b 5 15 a 2 b 5

641.

−4 y 52 −4 y 52

643.

p 2 + 3 p p 2 + 3 p

645.

−12 u 2 42 u −12 u 2 42 u

647.

9 q 4 63 q 3 + 54 q 2 9 q 4 63 q 3 + 54 q 2

649.

11 b 44 11 b 44

651.

12y244y+3512y244y+35 12y244y+3512y244y+35 12y244y+3512y244y+35

653.

y 2 12 y + 32 y 2 12 y + 32

655.

q 2 + 13 q 48 q 2 + 13 q 48

657.

u 4 + u 2 30 u 4 + u 2 30

659.

16 m 2 n 2 2 m n 3 16 m 2 n 2 2 m n 3

661.

18x321x234x+4018x321x234x+40 18x321x234x+4018x321x234x+40

663.

7 m 3 69 m 2 31 m 3 7 m 3 69 m 2 31 m 3

665.

q 2 30 q + 225 q 2 30 q + 225

667.

64 u 2 + 16 u + 1 64 u 2 + 16 u + 1

669.

16 a 2 24 a b + 9 b 2 16 a 2 24 a b + 9 b 2

671.

y 2 4 25 y 2 4 25

673.

36 r 2 36 r 2

675.

25 p 8 16 q 6 25 p 8 16 q 6

677.

36 a 2 121 36 a 2 121

679.

c 8 + 18 c 4 d + 81 d 2 c 8 + 18 c 4 d + 81 d 2

681.

4 a 3 a 2 b 2 + 16 a b 4 b 3 4 a 3 a 2 b 2 + 16 a b 4 b 3

683.

10 20 10 20

685.

1 v 36 1 v 36

687.

1 5 7 1 5 7

689.

1

691.

−1

693.

1

695.

0

697.

m 4 81 m 4 81

699.

x 6 64 y 6 x 6 64 y 6

701.

1

703.

r 20 r 20

705.

343 x 20 32 y 10 343 x 20 32 y 10

707.

10,125 n 10 4 10,125 n 10 4

709.

4 b 6 a 5 4 b 6 a 5

711.

9 p 2 9 p 2

713.

7 x 15 7 x 15

715.

55 p 3 30 p 55 p 3 30 p

717.

12 a 4 6 a 3 b 7 a b 2 12 a 4 6 a 3 b 7 a b 2

719.

21 y 2 + 10 1 y 2 21 y 2 + 10 1 y 2

721.

v 8 v 8

723.

n 6 + 4 n + 3 n 6 + 4 n + 3

725.

u 2 + 2 u + 4 u 2 + 2 u + 4

727.

1 125 1 125

729.

1 216 u 3 1 216 u 3

731.

16 9 16 9

733.

1 q 11 1 q 11

735.

1 y 8 1 y 8

737.

1 a 4 1 a 4

739.

r r

741.

4.29 × 10 −3 4.29 × 10 −3

743.

7.2 × 10 9 7.2 × 10 9

745.

15,000,000,000 15,000,000,000

747.

0.55 0.55

749.

0.0217 0.0217

751.

0.0000003 0.0000003

Practice Test

753.

15 a 2 + a 6 15 a 2 + a 6

755.

8 125 8 125

757.

16 a 6 b 10 16 a 6 b 10

759.

3 k 3 21 k 2 + 39 k 3 k 3 21 k 2 + 39 k

761.

9 v 2 86 v + 45 9 v 2 86 v + 45

763.

n 3 11 n 2 + 34 n 24 n 3 11 n 2 + 34 n 24

765.

49 p 2 25 49 p 2 25

767.

1 9 1 9

769.

1 1

771.

6 x + 21 3 x 6 x + 21 3 x

773.

16 x 2 + 4 x + 1 16 x 2 + 4 x + 1

775.

1 25 1 25

777.

1 q 9 1 q 9

779.

8.3 × 10 7 8.3 × 10 7

781.

74,800

783.

424 feet

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