Answers to Selected Exercises
© Cengage Learning. All rights reserved. No distribution allowed without express authorization.
Section A.1
1. set 3. union 5. decimal 7. 2 9. composite 11. decimals 13. negative 5. x 1 1y 1 z2 17. 5m 1 5 ? 2 19. interval 21. two 23. positive 25. true 27. false 29. true 31. 5 a, b, c, d, e, f, g 6 33. 5 a, c, e 6 35. terminates 37. repeats 39. 1, 2, 6, 7 41. 25, 24, 0, 1, 2, 6, 7 43. "2
45. 6 47. 25, 1, 7 49. –1
51. 53. 55. 0
1
2
3
4
5
10 11 12 13 14 15 16 17 18 19 20
−5 −4 −3 −2 −1
0
1
2
3
4
5
−6 −5 −4 −3 −2 −1
0
1
2
3
4
57. 12, ` 2 59. 10, 52 (
(
69. 3 22, 3 4 71. 3 2, 6 4 3
97. 3.72 3 105 99. 21.77 3 108 64
101. 7 3 1023 103. 26.93 3 1027 105. 1 3 1012 107. 937,000 109. 0.0000221 111. 3.2 113. 20.0032 115. 1.17 3 104 117. 7 3 104 119. 5.3 3 1019 121. 1.986 3 104 meters per min 123. 1.67248 3 10215 g 125. 9.3 3 107 mi, 1.48 3 108 mi 127. polar radius: 6.356750 3 103 km;
equatorial radius: 6.378135 3 103 km
129. xn12 131. xm21 133.xm14 137. 139. 5 2 p
(
)
93. 20 95. −2
(
[
−2
n
1. 0 3. not 5. a1/n 7. "ab 9. 2 11. 3 1
3
13. 15. 23 17. 10 19. 2 5
2
21. not a real number 23. 4 0 a 0 25. 2 0 a 0 2
]
5
]
−5
0
[
[
3
]
2
6
75. 3 28, ` 2 d 12`, 23 4 77. 12`, 222 c 12, ` 2 79. 12`, 21 4 c 3 3, ` 2 4a2
10x2
33. 2
50b0
3y
1
1
35. 8 37. 264 39. 2100 41. 43. 8
512
1
32
16
1
45. 2 47. 49. 51. 10s2 53. 2 27
9
2y z
243
1
4a4
100s8
55. x6y3 57. 6 12 59. 63. a 6 61. rs
25b
9r4
1
65. 7 67. 5 69. 25 71. 2 73. 6 0 x 0 5
0 x 0 y2
75. 3y2 77. 2y 79. 3 81. "2 83. 17x"2 0z 0
27. 22a 29. 26b2 31. ]
−2
4
Section A.3
)
(
73. 125, ` 2 d 12`, 42 (
)
−5
4
[
−8
]
–3
)
(
−2
]
−1
2
[
3
81. 13 83. 0 85. 28 87. 232 89. 5 2 p 91. 0 93. x 1 1 95. 2 1x 2 42 97. 5 99. 5 101. natural numbers 103. integers
Section A.2
83. 250 85. 4 87. 28 89. 216 91. 212 5
−4
65. 12`, 5 4 67. 125, 0 4 )
0
61. 124, ` 2 63. 3 22, 22 2
m9
1
a12
6 69. 9 71. 4 n
a
b
4y12
1
x32
9x10
64z7
73. 4 75. 16 77. 79. 20 81. 25y2
r
25y6
y
x
61. x4 63. a4 65. x 67. 1. factor 3. 3, 2x 5. scientific, integer 7. xm1n 9. xnyn 11. 1 13. 169 15. 225 17. 4 ? x ? x ? x 19. 125x2 125x2 125x2 125x2
21. 28 ? x ? x ? x ? x 23. 7x3 25. x2 27. 227t3 29. x3y2 31. 10.648 33. 20.0625 35. x5 37. z6 39. y21 41. z26 43. a14 45. 27x3 47. x6y3 a6
1
1
49. 3 51. 1 53. 1 55. 4 57. 5 59. x2 b
y
z
3
4
85. 2y2"3y 87. 12"3 89. 6z"3z 91. 6x"2y 93. 0 95. "3 97. 2"x
3
3
99. "
4 101. "
5a2
x
4
3
2b"
27a2
u"
6uv2
1
1
105. 107. 109. 3 3a
3v
2"5
"3
2"3
"2x
b
113. 115. 2
117. "3 111. 5
9
8
32a"
2b2
4
"12
5
6
129. 122, 5 4 119. "4x3 121. "32 123. 2
131. 25 133. 6.17 3 108
103. Section A.4
Not For Sale
90905_em-ans_A1-A35.indd 1
1. monomial, variables 3. trinomial 5. one 7. like 9. coefficients, variables 11. yes, trinomial, 2nd degree Ans1
11/17/11 2:06 PM
Not For Sale
Answers to Selected Exercises
13. no 15. yes, binomial, 3rd degree 17. yes, monomial,
0th degree 19. yes, monomial, no defined degree
21. 6x3 2 3x2 2 8x 23. 4y3 1 14 25. 2x2 1 14
27. 228t 1 96 29. 24y2 1 y 31. 2x2y 2 4xy2
m 4n 4
33. 8x3y7 35. 37. 24r3s 2 4rs3
2
39. 12a2b2c2 1 18ab3c3 2 24a2b4c2 41. a2 1 4a 1 4 43. a2 2 12a 1 36 45. x2 2 16 47. x2 1 2x 2 15 49. 3u2 1 4u 2 4 51. 10x2 1 13x 2 3 53. 9a2 2 12ab 1 4b2 55. 9m2 2 16n2 57. 6y2 2 16xy 1 8x2 59. 9x3 2 x2y 2 27xy 1 3y2 61. 5z3 2 5tz 1 2tz2 2 2t2 63. 23"5x2 1 x 1 2"5
65. 27x3 2 27x2 1 9x 2 1 67. 6x3 1 14x2 2 5x 2 3
69. 6x3 2 5x2y 1 6xy2 1 8y3 71. 6y2n 1 2
73. 210x4n 2 15y2n 75. x2n 2 xn 2 12
77. 6r2n 2 25rn 1 14 79. xy 1 x3/2y1/2
81. a 2 b 83. "3 1 1 85. xQ"7 2 2R 87. xQx 1 "3R
x2 2 3
89. Qy 1 "2R
y2 2 2
2
x 2 2"xy 1 y
"3 1 3 2 "2 2 "6
93. 2
x2y
y2 2 3
1
95. 97. 2
y 1 2y"3 1 3
2Q"2 2 1R
1
2a
2z9
101. 3 103. 2 3 2 99. b
3x y
"x 1 3 1 "x
91. 3xy
2y3
3y
1
x
1
107. 2 3 1 4 3 109. 3x 1 2
2y
2
5
5x
5x y
2
3
2
111. x 2 7 1
113. 2x 1 2x 1 2 1
2x 2 5
x21
2
2x 1 5
115. x 2 3 117. x2 2 2 1 3
x 22
4
3
2
119. x 1 2x 1 4x 1 8x 1 16 121. 6x2 1 x 2 12
123. 1x2 1 3x 2 102 ft2 125. 14x3 2 48x2 1 144x2 in.3
125x3
3
133. 27 135. 137. 2b"
2ab
8y6
105. Section A.5
1. factor 3. x 1a 1 b2 5. 1x 1 y2 2
7. 1x 1 y2 1x2 2 xy 1 y22 9. 3 1x 2 22 11. 4x2 12 1 x2 13. 7x2y2 11 1 2x2 15. 1x 1 y2 1a 1 b2 17. 14a 1 b2 11 2 3a2 19. 12x 1 32 12x 2 32 21. 12 1 3r2 12 2 3r2 23. 19x2 1 12 13x 1 12 13x 2 12 25. 1x 1 z 1 52 1x 1 z 2 52 27. 1x 1 42 2 29. 1b 2 52 2 31. 1m 1 2n2 2 33. 14x 2 3y2 13x 1 2y2 35. 1x 1 72 1x 1 32 37. 1x 2 62 1x 1 22 39. 12p 1 32 13p 2 12
41. 1t 1 72 1t2 2 7t 1 492 43. 12z 2 32 14z2 1 6z 1 92
45. 3abc 1a 1 2b 1 3c2 47. 1x 1 12 13x2 2 12
49. t 1y 1 c2 12x 2 32 51. 1a 1 b2 1x 1 y 1 z2
53. 1x 1 y 2 z2 1x 2 y 1 z2 55. 24xy
57. 1x2 1 y22 1x 1 y2 1x 2 y2 59. 3 1x 1 22 1x 2 22
61. 2x 13y 1 22 13y 2 22 63. prime 65. 16a 1 52 14a 2 32 67. 13x 1 7y2 12x 1 5y2 69. 2 16p 2 35q2 1p 1 q2 71. 2 16m 2 5n2 1m 2 7n2
73. 2x 16x 1 72 1x 2 52 75. x2 12x 2 72 13x 1 52
77. 1x2 1 52 1x2 2 32 79. 1an 2 32 1an 1 12 90905_em-ans_A1-A35.indd 2
81. 13xn 2 22 12xn 2 12 83. 12xn 1 3yn2 12xn 2 3yn2
85. 15yn 1 22 12yn 2 32 87. 2 1x 1 102 1x2 2 10x 1 1002
89. 1x 1 y 2 42 1x2 1 2xy 1 y2 1 4x 1 4y 1 162
91. 12a 1 y2 12a 2 y2 14a2 2 2ay 1 y22 14a2 1 2ay 1 y22
93. 1a 2 b2 1a2 1 ab 1 b2 1 12
95. 14x2 1 y22 116x4 2 4x2y2 1 y42 97. 1x 2 3 1 12y2 1x 2 3 2 12y2 99. 1a 1 b 2 52 1a 1 b 1 22
101. 1x 1 22 1x2 2 2x 1 42 1x 2 12 1x2 1 x 1 12
103. 1x2 1 1 1 x2 1x2 1 1 2 x2
105. 1x2 1 x 1 42 1x2 2 x 1 42
107. 12a2 1 a 1 12 12a2 2 a 1 12
4
3
109. p 1r1 2 r22 1r21 1 r1r2 1 r222 115. 2a x 1 1b
2
3
b
1 2
117. 2a x 1 x 1 2b 119. aa1 1 b 121. x1/2 1x1/2 1 12
2
a
123. "2Q"2x 1 yR 125. ab 1b1/2 2 a1/22 127. 1x 2 22 1x 1 3 1 y2 129. 1a 1 12 1a3 1 a2 1 12 131. 1 133. x20 135. 1 137. 23"5x
Section A.6
ac
a1c
7. bd
b
a
8x
9. equal 11. not equal 13. 15. 3b
35a
2
2x y
16
z
2
17. 19. 21. 2 3 23. 3
c
ab
x12
1. numerator 3. ad 5 bc 5. 25. 2
3x 2 4
x2 1 2x 1 4
x12
27. 29. x23
2x 2 1
x1a
x21
x 1x 1 12 2
x 1x 2 12
33. 35. x11
x
x12
1
z24
37. 39. 41. 1 43. 1
1z 1 22 1z 2 22
2
x25
x15
21
45. 47. 49. 4 51. x25
x15
x13
2 1a 2 22
5x 2 1
55. 53. 1x 1 12 1x 2 12
1a 1 42 1a 2 42
2
2 1x2 2 3x 1 12
57. 59. 1x 1 12 2 1x 2 12
1x 1 22 1x 2 22
31. 3y 2 2
1
2x 2 5
63. 65. y21
x12
2x 1x 2 22
2x2 1 19x 1 1
67. 69. 0
1x 1 42 1x 2 42
61. © Cengage Learning. All rights reserved. No distribution allowed without express authorization.
Ans2
b
2x4 1 3x3 2 43x2 2 58x 1 697
73. 1x 1 52 1x 2 52 1x 1 42 1x 2 42
2c
y1x
y1x
75. 81a 77. 21 79. 2 2 81. xy
y2x
71. 83. 89. 3x2y2
x22
a2 13x 2 4ab2
85. 87. ax 1 b
x12
xy 2 1
x2 2 3x 2 4
x
3x2
91. 2
93. x 11
x 1 5x 2 3
x11
2
k1k2
3x
5x 1 1
97. 99. x21
k2 1 k1
31x
9
y
x11
101. 107. 6 109. 12 111. 2"5
2x 1 1
x
95. 11/17/11 2:07 PM
Answers to Selected Exercises
© Cengage Learning. All rights reserved. No distribution allowed without express authorization.
Chapter Review
x 2 2"xy 1 y
x2y
y
12a
107. 108. 109. 2x
5Q"x 2 2R
aQ1 1 "aR
1. 3, 6, 8 2. 0, 3, 6, 8 3. 26, 23, 0, 3, 6, 8
1
4. 26, 23, 0, , 3, 6, 8 5. p, "5 2
1
6. 26, 23, 0, , 3, p, "5, 6, 8 7. 3 8. 6, 8
2
9. 26, 0, 6, 8 10. 23, 3
11. Associative Property of Addition
12. Commutative Property of Addition
13. Associative Property of Multiplication
14. Distributive Property
15. Commutative Property of Multiplication
16. Commutative Property of Addition
17. Double Negative Rule
18. 105. 6 7 8 9 10 11 12 13 14
(
20. 22. ]
−3
(
]
−2
23. 4
)
24. −4
)
21. 5
(
−1
−5
[
)
0
2
133. [
6
135. 25. 6 26. 25 27. "2 2 1 28. "3 2 1
29. 12 30. 25aaa 31. 125a2 125a2 32. 3t3
33. 26b2 34. n6 35. p6 36. x12y8 37. 137. q6
1
1
b6
a12
6 38. 6 39. 6 40. 3 41. 4
a
b
m
8p
a
y8
y4
a8
8m12
43. 10 44. 4 45. 2 3 9
n
b
9x
46. 18 47. 6.75 3 103 48. 2.3 3 1024
49. 480 50. 0.00025 51. 1.5 3 1014 52. 11
3
53. 54. 2x 55. 3 0 a 0 56. 210x2 5
y2
57. not a real number 58. x6 0 y 0 59. 6
x
1
8
4
2
60. 2c 61. a 62. 16 63. 64. 65. 8
27
9
9
125
66. 67. 68. 36x2 69. p2a/3 70. 6 4
8
3
3
71. 27 72. 73. 74. 0 x 0 y2 75. x 5
5
a 3b 2
m2 0 n 0
3
77. 3x 78. 7"2 79. 0 80. x"
76. c
p4
85. 3
3
"
4
2"
5
"35
82. 2"2 83. 84. 5
2
5
2
5"2
86. 1
"5
87. 2x
3"2x
88. 21x
3
2"
49x2
106. 89. 3rd degree, binomial 90. 2nd degree, trinomial
91. 2nd degree, monomial 92. 4th degree, trinomial
93. 5x 2 6 94. 2x3 2 7x2 2 6x 95. 9x2 1 12x 1 4 96. 6x2 2 7xy 2 3y2 97. 8a2 2 8ab 2 6b2 98. 3z3 1 10z2 1 2z 2 3 99. a2n 1 an 2 2 100. 2 1 2x"2 1 x2 101. "6 1 "2 1 "3 1 1 1x 2 22 1x 1 32 1x 2 32
134. 1
1x 2 12 1x 1 22 2
2 12x2 1 3x 1 62
3x2 2 10x 1 10
136. 1x 2 42 1x 1 52
1x 1 22 1x 2 22
3x3 2 12x2 1 11x
25x 2 6
138. 1x 2 12 1x 2 22 1x 2 32
1x 1 12 1x 1 22
2x3 1 x2 2 12x 2 15
3x
140. x2 1x 1 12
x11
y1x
y
y1x
20
141. 142. 143. 144. 3x
2
xy 1x 2 y2
x2y
139. 42. 81. x24
x24
110. 2a2b 1 3ab2 111. x2 1 2x 1 1
6
113. 3t 1t 1 12 1t 2 12 112. x3 1 2x 2 3 2 2
x 21
114. 5 1r 2 12 1r2 1 r 1 12 115. 13x 1 82 12x 2 32 116. 13a 1 x2 1a 2 12 117. 12x 2 52 14x2 1 10x 1 252 118. 2 13x 1 22 1x 2 42 119. 1x 1 3 1 t2 1x 1 3 2 t2 120. prime 121. 12z 1 72 14z2 2 14z 1 492 122. 17b 1 12 2 123. 111z 2 22 2 124. 8 12y 2 52 14y2 1 10y 1 252 125. 1y 2 2z2 12x 2 w2 126. 1x2 1 1 1 x2 1x2 1 1 2 x2 1x4 1 1 2 x22
21
a13
127. 128. 129. 1x 2 22 1x 1 32 x22
a23
2y 2 5
p 1p 1 42
t11
130. 131. 132. 2
1p 1 8p 1 42 1p 2 32
y22
5
10 11 12 13 14 15 16 17 18 19 20
19. 2xQ"x 1 2R
Ans3
Chapter Test
1. 27, 1, 3 2. 3 3. Commutative Property of
Addition 4. Distributive Property (
]
)
[
5. 6. −4
2
−3
6
7. 17 8. 2 1x 2 72 9. 16 10. 8 11. x11
r
12. 13. a 14. x24 15. 4.5 3 105 s
16. 3.45 3 1024 17. 3,700 18. 0.0012
216
9s6
21. 4 22. 3a2
19. 5a2 20. 729
4t
xQ"x 1 2R
3
23. 5"3 24. 24x"
3x 25. x24
x2y
26. 27. 2a2 1 7 28. 26a6b6
x 1 2"xy 1 y
29. 6x2 1 13x 2 28 30. a2n 2 an 2 6 31. x4 2 16 34
32. 2x3 2 5x2 1 7x 2 6 33. 6x 1 19 1
x23
34. x2 1 2x 1 1 35. 3 1x 1 2y2 36. 1x 1 102 1x 2 102
37. 15t 2 2w2 12t 2 3w2 38. 3 1a 2 62 1a2 1 6a 1 362
39. 1x 1 22 1x 2 22 1x2 1 32 40. 13x2 2 22 12x2 1 52
1x 1 52 2
22x
41. 1 42. 43. 1x 1 12 1x 2 12
x14
y
1
b1a
44. 46. 45. 1x 1 12 1x 2 22
y1x
a
Not For Sale
102. 25 103. "3 1 1 104. 22Q"3 1 "2R
90905_em-ans_A1-A35.indd 3
11/17/11 2:07 PM