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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  14. 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
    11. Chapter 11
    12. Chapter 12
  15. Index

Be Prepared

5.1

11 x 2 + 8 x + 6 11 x 2 + 8 x + 6

5.2

3 n + 9 3 n + 9

5.3

200 200

5.4

8 8

5.5

x 3 y x 3 y

5.6

10.946 10.946

5.7

2 x + 6 2 x + 6

5.8

8181; 8181; 8181

5.9

21 21

5.10

3 + x d 3 + x d

5.11

6 y 2 6 y 2

5.12

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

Try It

5.1

monomial, 0
polynomial, 3 trinomial, 4
binomial, 2 monomial, 10

5.2

binomial, 3 trinomial, 3 monomial, 0 polynomial, 4 monomial, 7

5.3

21q221q2 13mn313mn3

5.4

−7c2−7c2 −10y2z3−10y2z3

5.5

5y2+3z25y2+3z2
m2n28m2+4n2m2n28m2+4n2

5.6

−4m2+n2−4m2+n2
pq26p5q2pq26p5q2

5.7

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

5.8

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

5.9

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

5.10

6 b 2 + 3 6 b 2 + 3

5.11

−5ab+7b2−5ab+7b2

5.12

7mn+4n27mn+4n2

5.13

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

5.14

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

5.15

x 3 - y 3 x 3 - y 3

5.16

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

5.17

18 50 −15−15

5.18

20 2 −4−4

5.19

The height is 150150 feet.

5.20

The height is 31 feet.

5.21

(f+g)(x)=3x26x3(f+g)(x)=3x26x3 (f+g)(3)=6(f+g)(3)=6
(fg)(x)=x22x+9(fg)(x)=x22x+9
(fg)(−2)=17(fg)(−2)=17

5.22

(f+g)(x)=6x2x+7(f+g)(x)=6x2x+7 (f+g)(3)=58(f+g)(3)=58
(fg)(x)=4x27x9(fg)(x)=4x27x9
(fg)(−2)=21(fg)(−2)=21

5.23

b17b17 43x43x 12p612p6
x18x18

5.24

x16x16 10x+110x+1 12z812z8
b19b19

5.25

x5x5 6969 1x41x4
1121511215

5.26

y6y6 108108 1m81m8
19111911

5.27

1 1

5.28

1 1

5.29

1z31z3 11071107 p8p8 6464

5.30

1n21n2 110,000110,000 q7q7
1616

5.31

81168116 n2m2n2m2

5.32

1252712527 b4a4b4a4

5.33

1z91z9 1p3q31p3q3 12v5u12v5u

5.34

1c151c15 1r2s81r2s8 30d3c830d3c8

5.35

b35b35 512512 a48a48

5.36

z54z54 349349 q29q29

5.37

32w5x532w5x5 1 116b12116b12
64a864a8

5.38

−27y3−27y3 1 116x8116x8
8c128c12

5.39

p410000p410000 n7m7n7m7
81a4b12c881a4b12c8 27x6y927x6y9

5.40

−8q3−8q3 x4w4x4w4 x2y69z4x2y69z4
8n6m68n6m6

5.41

81c24d3081c24d30 1a181a18
y15y15

5.42

256a22b24256a22b24 1p391p39
2x3y102x3y10

5.43

9.6×1049.6×104 7.8×10−37.8×10−3

5.44

4.83×1044.83×104
1.29×10−21.29×10−2

5.45

1,300 −0.00012−0.00012

5.46

−950,000−950,000 0.075

5.47

−0.006−0.006 20,000

5.48

−0.009−0.009 400,000

5.49

−35y11−35y11 6a5b66a5b6

5.50

54b954b9 8r11s88r11s8

5.51

−15y324y2+21y−15y324y2+21y
12x4y220x3y3+12x2y412x4y220x3y3+12x2y4

5.52

8x424x3+20x28x424x3+20x2
−18a5b+12a4b236a3b3−18a5b+12a4b236a3b3

5.53

x2+17x+72x2+17x+72
15c2+14c815c2+14c8

5.54

20x2+51x+2720x2+51x+27
30y23y630y23y6

5.55

x22x35x22x35
15x2+29x1415x2+29x14

5.56

b2+3b18b2+3b18
16y220y5016y220y50

5.57

x38x2+6x48x38x2+6x48
8a2b2+12ab208a2b2+12ab20

5.58

y39y2+7y63y39y2+7y63
8x2y2+2xy158x2y2+2xy15

5.59

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

5.60

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

5.61

y38y2+17y6y38y2+17y6
y38y2+17y6y38y2+17y6

5.62

2x3+5x27x+202x3+5x27x+20
y38y2+17y6y38y2+17y6

5.63

x2+18x+81x2+18x+81
4c24cd+d24c24cd+d2

5.64

y2+22y+121y2+22y+121
16x240xy+25y216x240xy+25y2

5.65

36x22536x225
16p249q216p249q2

5.66

4x2494x249 9x2y29x2y2

5.67

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

5.68

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

5.69

(f·g)(x)=x37x2+13x15(f·g)(x)=x37x2+13x15
(f·g)(2)=−9(f·g)(2)=−9

5.70

(f·g)(x)=x3+x252x28(f·g)(x)=x3+x252x28
(f·g)(2)=−120(f·g)(2)=−120

5.71

9 a 5 b 9 a 5 b

5.72

−9 d c 4 −9 d c 4

5.73

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

5.74

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

5.75

−4 a + 2 b −4 a + 2 b

5.76

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

5.77

y + 7 y + 7

5.78

m + 5 m + 5

5.79

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

5.80

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

5.81

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

5.82

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

5.83

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

5.84

4 x 2 3 x + 1 ; 1 4 x 2 3 x + 1 ; 1

5.85

x 3 4 x 2 + 5 ; 0 x 3 4 x 2 + 5 ; 0

5.86

x 3 3 x 2 + 2 ; 0 x 3 3 x 2 + 2 ; 0

5.87

(fg)(x)=x8(fg)(x)=x8
(fg)(−3)=−11(fg)(−3)=−11

5.88

(fg)(x)=x9(fg)(x)=x9
undefined

5.89

−1 −1

5.90

6 6

5.91

yes

5.92

yes

Section 5.1 Exercises

1.

trinomial, 5 polynomial, 3 binomial, 2 monomial, 0
binomial, 2

3.

binomial, 1 trinomial, 2
polynomial, 3 trinomial, 5
monomial, 0

5.

trinomial, 2trinomial, 2 monomial, 4monomial, 4 binomial, 1binomial, 1 polynomial, 3polynomial, 3
monomial, 0monomial, 0

7.

binomial, 1binomial, 1 trinomial, 2trinomial, 2 polynomial, 3polynomial, 3 binomial, 3binomial, 3
monomial, 0monomial, 0

9.

12x212x2 5a5a

11.

6w6w 19x2y19x2y

13.

12x 2 5a 12x 2 5a

15.

6 w + 19 x 2 y 6 w + 19 x 2 y

17.

−22b−22b 16xy16xy

19.

−10a+5b−10a+5b
pq24p3q2pq24p3q2

21.

−4a2+b2−4a2+b2
x2y3x+7xy2x2y3x+7xy2

23.

xy25x5y2xy25x5y2
19y+5z19y+5z

25.

x 3 y + a 2 b 4 a 5 a b 2 x 3 y + a 2 b 4 a 5 a b 2

27.

u 2 + 4 v 2 + 12a + 8 b u 2 + 4 v 2 + 12a + 8 b

29.

4a 3 b 4a 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.

11 w 66 11 w 66

53.

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

55.

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

57.

−3 a b + 3 b 2 −3 a b + 3 b 2

59.

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

61.

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

63.

187 40 2

65.

−104−104 4 40

67.

The height is 11 feet.

69.

The revenue is $10,800.

71.

The cost is $456.

73.

(f+g)(x)=7x2+4x+4(f+g)(x)=7x2+4x+4 (f+g)(2)=40(f+g)(2)=40
(fg)(x)=−3x212x2(fg)(x)=−3x212x2
(fg)(−3)=7(fg)(−3)=7

75.


 (f+g)(x)=6x3x29x+3(f+g)(x)=6x3x29x+3
(f+g)(2)=29(f+g)(2)=29
(fg)(x)=x2+5x+3(fg)(x)=x2+5x+3
(fg)(−3)=−21(fg)(−3)=−21

77.

Answers will vary.

79.

Answers will vary.

Section 5.2 Exercises

81.

d9d9 414x414x 8y48y4 w6w6

83.

n31n31 3x+63x+6 56w656w6
a16a16

85.

m x + 3 m x + 3

87.

y a + b y a + b

89.

x15x15 5959 1q181q18 110110

91.

p14p14 412412 1b81b8 145145

93.

1 1

95.

−1−1 −1−1

97.

1a21a2 1100011000 c5c5 99

99.

1r31r3 1100,0001100,000 q10q10
1,0001,000

101.

64256425 a2b2a2b2

103.

7296472964 v5u5v5u5

105.

125125 125125 2525 −25−25

107.

3535 115115

109.

1b41b4 w2x9w2x9 −12cd4−12cd4

111.

1 1u4v51u4v5 36r2s536r2s5

113.

1 p 1 p

115.

m8m8 10181018 1x121x12

117.

y3xy3x 5xy5xy 1q481q48

119.

9x2y29x2y2 1 125x4125x4
16y616y6

121.

−125a3b3−125a3b3 1 136x6136x6 9y89y8

123.

p532p532 y6x6y6x6 8x3y6z38x3y6z3
16p6q416p6q4

125.

a481b4a481b4 16m22516m225 a4c49b6a4c49b6 q8r8p2q8r8p2

127.

1125t81125t8 1t191t19 y43x2y43x2

129.

16m8n2216m8n22 4p64p6

131.

7n7n 17n17n 17n17n

133.

19p219p2 3p23p2 −3p2−3p2

135.

x 14 x 14

137.

a 36 a 36

139.

8 m 18 8 m 18

141.

1,000 x 6 y 3 1,000 x 6 y 3

143.

16 a 12 b 8 16 a 12 b 8

145.

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

147.

1,024 a 10 1,024 a 10

149.

25,000 p 24 25,000 p 24

151.

x 18 y 18 x 18 y 18

153.

144 m 8 n 22 144 m 8 n 22

155.

45x345x3 48y448y4

157.

12r412r4 13x1113x11

159.

1 j 3 1 j 3

161.

4000 n 12 4000 n 12

163.

3.4×1053.4×105 4.1×10−24.1×10−2

165.

1.29×1061.29×106
1.03×10−61.03×10−6

167.

−830−830 0.038

169.

16,000,000,000
0.00000843

171.

0.02 500,000,000

173.

0.0000056 20,000,000

175.

Answers will vary.

177.

Answers will vary.

Section 5.3 Exercises

179.

30x830x8 15x8y215x8y2

181.

72c572c5 13m5n513m5n5

183.

−5t315t2+90t−5t315t2+90t
9sr527s2r4+45s3r39sr527s2r4+45s3r3

185.

−5m315m2+90m−5m315m2+90m
−21x4y230x3y3+3x2y4−21x4y230x3y3+3x2y4

187.

y 2 + 12 y + 27 y 2 + 12 y + 27

189.

21 q 2 44 q 32 21 q 2 44 q 32

191.

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

193.

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

195.

m 2 + 7 m 44 m 2 + 7 m 44

197.

33 r 2 85 r 8 33 r 2 85 r 8

199.

y 3 + 3 y 2 4 y 12 y 3 + 3 y 2 4 y 12

201.

6 x 2 y 2 + 13 x y + 6 6 x 2 y 2 + 13 x y + 6

203.

y 4 11 y 2 + 28 y 4 11 y 2 + 28

205.

9 r 2 s 2 33 r s + 28 9 r 2 s 2 33 r s + 28

207.

u 3 + 7 u 2 + 14 u + 8 u 3 + 7 u 2 + 14 u + 8

209.

3 a 3 + 31 a 2 + 5 a 50 3 a 3 + 31 a 2 + 5 a 50

211.

6 a 4 13 a 3 + 15 a 2 + 35 a 50 6 a 4 13 a 3 + 15 a 2 + 35 a 50

213.

p 3 10 p 2 + 33 p 36 p 3 10 p 2 + 33 p 36

215.

6 r 3 41 r 2 61 r 9 6 r 3 41 r 2 61 r 9

217.

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

219.

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

221.

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

223.

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

225.

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

227.

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

229.

64j216 64 j 2 16

231.

81 c 2 25 81 c 2 25

233.

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

235.

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

237.

x2y281 x 2 y 2 81

239.

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

241.

t 2 18 t + 81 t 2 18 t + 81

243.

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

245.

9 p 2 64 9 p 2 64

247.

k 2 12 k + 36 k 2 12 k + 36

249.

8 x 3 x 2 y 2 + 64 x y 8 y 3 8 x 3 x 2 y 2 + 64 x y 8 y 3

251.

y 8 + 4 y 4 z + 4 z 2 y 8 + 4 y 4 z + 4 z 2

253.

m 6 16 m 3 n + 64 n 2 m 6 16 m 3 n + 64 n 2

255.

r 5 + r 2 s 2 r 3 s 3 s 5 r 5 + r 2 s 2 r 3 s 3 s 5

257.

18 p 9 18 p 9

259.

−10 j 15 −10 j 15

261.

9 d 7 9 d 7

263.

42 m 5 n 8 42 m 5 n 8

265.

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

267.

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

269.

6 k 3 + 11 k 2 26 k + 4 6 k 3 + 11 k 2 26 k + 4

271.

121 b 2 121 b 2

273.

4 x 4 9 y 8 4 x 4 9 y 8

275.

9 d 2 + 6 d + 1 9 d 2 + 6 d + 1

277.

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

279.


(f·g)(x)=4x3x28x+5(f·g)(x)=4x3x28x+5
(f·g)(−2)=−15(f·g)(−2)=−15

281.

(f·g)(x)=49x264(f·g)(x)=49x264
(f·g)(−2)=132(f·g)(−2)=132

283.


 (f·g)(x)=x4+6x3+9x2+10x12(f·g)(x)=x4+6x3+9x2+10x12 (f·g)(1)=14(f·g)(1)=14

285.

Answers will vary.

287.

Answers will vary.

Section 5.4 Exercises

289.

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

291.

−3 y 3 4 x 3 −3 y 3 4 x 3

293.

−3 q 5 p 5 −3 q 5 p 5

295.

5 v 4 u 2 5 v 4 u 2

297.

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

299.

−6 y 2 + 3 y −6 y 2 + 3 y

301.

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

303.

−5 y 3 + 1 4 y −5 y 3 + 1 4 y

305.

a 7 a 7

307.

4 x + 3 4 x + 3

309.

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

311.

2 n 2 6 n + 8 + 4 n + 3 2 n 2 6 n + 8 + 4 n + 3

313.

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

315.

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

317.

x 2 5 x + 6 ; 0 x 2 5 x + 6 ; 0

319.

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

321.

x 3 2 x 2 + 5 x 4 ; 2 x 3 2 x 2 + 5 x 4 ; 2

323.

3 x 3 2 x 2 4 x 2 ; 0 3 x 3 2 x 2 4 x 2 ; 0

325.

(fg)(x)=x6(fg)(x)=x6
(fg)(−5)=−11(fg)(−5)=−11

327.

(fg)(x)=x2+5x4(fg)(x)=x2+5x4
(fg)(0)=−4(fg)(0)=−4

329.


 (f·g)(x)=x4+6x3+9x2+10x12;(f·g)(x)=x4+6x3+9x2+10x12; (f·g)(1)=14(f·g)(1)=14

331.

−9 −9

333.

−6

335.

no

337.

yes

339.

answer will vary

341.

Answers will vary.

Review Exercises

343.

binomial

345.

trinomial

347.

−13 y 3 −13 y 3

349.

6 m 2 + 19 m 4 6 m 2 + 19 m 4

351.

5 u 2 + 4 u + 7 5 u 2 + 4 u + 7

353.

14 x 7 14 x 7

355.

−7 b 3 a −7 b 3 a

357.

8 a 2 5 a 2 8 a 2 5 a 2

359.

3 m 2 3 m + 3 3 m 2 3 m + 3

361.

3 y 2 8 y 14 3 y 2 8 y 14

363.

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

365.

165 39 5

367.

The height is 64feet64feet.

369.

(f+g)(x)=4x25x2(f+g)(x)=4x25x2 (f+g)(3)=19(f+g)(3)=19
(fg)(x)=−3x12(fg)(x)=−3x12
(fg)(−2)=−6(fg)(−2)=−6

371.

p 13 p 13

373.

a 6 a 6

375.

y a + b y a + b

377.

a 5 a 5

379.

1 x 5 1 x 5

381.

1

383.

−3 −3

385.

1 1000 1 1000

387.

1 8 n 1 8 n

389.

1 1000 1 1000

391.

36

393.

−125 −125

395.

1 125 1 125

397.

x 3 27 x 3 27

399.

3 10 3 10

401.

x 6 x 6

403.

1 u 3 v 5 1 u 3 v 5

405.

1 p 1 p

407.

1 q 16 1 q 16

409.

n 2 n 2

411.

1

413.

9 y 8 9 y 8

415.

81 x 4 y 8 z 4 81 x 4 y 8 z 4

417.

27 x 7 y 17 27 x 7 y 17

419.

3 y 4 4 x 4 3 y 4 4 x 4

421.

5.3 × 10 6 5.3 × 10 6

423.

29,000 29,000

425.

0.00009413 0.00009413

427.

0.00072 0.00072

429.

9,000 9,000

431.

10 c 10 10 c 10

433.

m 7 n 10 9 m 7 n 10 9

435.

a 4 9 a 3 36 a 2 a 4 9 a 3 36 a 2

437.

8 n 4 10 n 3 8 n 4 10 n 3

439.

y 2 + 8 y 48 y 2 + 8 y 48

441.

18 p 2 93 p + 110 18 p 2 93 p + 110

443.

k 2 3 k 54 k 2 3 k 54

445.

10 y 2 59 y + 63 10 y 2 59 y + 63

447.

x 2 + x 72 x 2 + x 72

449.

30 a 2 33 a + 3 30 a 2 33 a + 3

451.

15 b 3 b 2 47 b + 18 15 b 3 b 2 47 b + 18

453.

24 y 3 54 y 2 + 32 y 5 24 y 3 54 y 2 + 32 y 5

455.

x 2 + 3 2 x + 9 16 x 2 + 3 2 x + 9 16

457.

25 p 2 + 70 p q + 49 q 2 25 p 2 + 70 p q + 49 q 2

459.

36 x 2 y 2 36 x 2 y 2

461.

144 x 6 49 y 4 144 x 6 49 y 4

463.

9 p 9 9 p 9

465.

3 y 4 3 y 4

467.

4 a 5 b 2 4 a 5 b 2

469.

4 m 9 n 4 4 m 9 n 4

471.

−9 y 2 + 4 y −9 y 2 + 4 y

473.

−3 x 1 + 3 4 x −3 x 1 + 3 4 x

475.

y 3 + 33 y + 5 y 3 + 33 y + 5

477.

a 2 a + 1 2 a + 1 a 2 a + 1 2 a + 1

479.

2 x 2 5 x 4 ; 0 2 x 2 5 x 4 ; 0

481.

(fg)(x)=x6(fg)(x)=x6
(fg)(−2)=−8(fg)(−2)=−8

483.

−9 −9

485.

no

Practice Test

487.

trinomial 4

489.

6 x 2 3 x + 11 6 x 2 3 x + 11

491.

x x

493.

1 1

495.

1 8 y 3 1 8 y 3

497.

x 9 x 9

499.

4 r s 6 4 r s 6

501.

−48 x 5 y 9 −48 x 5 y 9

503.

7 m 2 + 19 m 6 7 m 2 + 19 m 6

505.

16 x 2 24 x + 9 16 x 2 24 x + 9

507.

3 y 2 7 x 3 y 2 7 x

509.

yes

511.

4.8 × 10 3 4.8 × 10 3

513.

3636 2121 99

515.

(fg)(x)=3x+4(fg)(x)=3x+4
(fg)(3)=13(fg)(3)=13

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