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Mathematics LibreTexts

12.4.10: Chapter 10

  • Page ID
    119031
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    Be Prepared

    10.1

    11 x 11 x

    10.2

    3 n + 9 3 n + 9

    10.3

    100 100

    10.4

    9 16 9 16

    10.5

    8 8

    10.6

    2 x + 6 2 x + 6

    10.7

    44 + 33 a 44 + 33 a

    10.8

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

    10.9

    1 3 1 3

    10.10

    32 m 15 32 m 15

    10.11

    x y x y

    10.12

    ten thousand

    10.13

    twelve ten-thousandths

    10.14

    8 8

    10.15

    2 2 2 7 2 2 2 7

    10.16

    18 a 33 18 a 33

    10.17

    4 x 4 + 12 x 3 4 x 2 4 x 4 + 12 x 3 4 x 2

    Try It

    10.1
    1. monomial
    2. polynomial
    3. trinomial
    4. binomial
    5. monomial
    10.2
    1. binomial
    2. trinomial
    3. polynomial
    4. monomial
    5. monomial
    10.3
    1. 1
    2. 1
    3. 4
    4. 2
    5. 0
    10.4
    1. 0
    2. 2
    3. 4
    4. 5
    5. 3
    10.5

    17x2

    10.6

    −3y2

    10.7

    14n

    10.8

    −2a3

    10.9

    −2x2 + 3y2

    10.10

    −2a2 + b2

    10.11

    4x2 − 8x + 10

    10.12

    11y2 + 9y − 5

    10.13

    3y2 + 3y + 3

    10.14

    3u2u + 2

    10.15

    4n2 + 12n

    10.16

    5a2 + 8a + 8

    10.17
    1. 13
    2. 3
    10.18
    1. 114
    2. −2
    10.19

    4 feet

    10.20

    20 feet

    10.21
    1. 64
    2. 11
    10.22
    1. 81
    2. 21
    10.23
    1. 25 64 25 64
    2. 0.4489 0.4489
    10.24
    1. 8 125 8 125
    2. 0.016129 0.016129
    10.25
    1. 16
    2. −16
    10.26
    1. 64
    2. −64
    10.27

    x 15

    10.28

    x 16

    10.29

    p 10

    10.30

    m 8

    10.31

    610

    10.32

    915

    10.33

    y 43

    10.34

    z 39

    10.35

    x 21

    10.36

    y 15

    10.37
    1. x 28
    2. 732
    10.38
    1. x 54
    2. 842
    10.39

    196x2

    10.40

    144a2

    10.41

    256x4y4

    10.42

    216x3y3

    10.43

    x 40

    10.44

    y 42

    10.45

    −512x12y21

    10.46

    81a20b24

    10.47

    98n14

    10.48

    48m5

    10.49

    64u18v22

    10.50

    675x7y18

    10.51

    −56x11

    10.52

    54y9

    10.53

    12m5n6

    10.54

    12p11q8

    10.55

    6x + 48

    10.56

    2y + 24

    10.57

    y2 − 9y

    10.58

    p2 − 13p

    10.59

    8x2 + 24xy

    10.60

    18r2 + 3rs

    10.61

    −32y3 − 20y2 + 36y

    10.62

    −54x3 − 6x2 + 6x

    10.63

    12x4 − 9x3 + 27x2

    10.64

    24y4 − 16y3 − 32y2

    10.65

    xp + 8p

    10.66

    ap + 4p

    10.67

    x2 + 17x + 72

    10.68

    a2 + 9a + 20

    10.69

    20x2 + 51x + 27

    10.70

    80m2 + 142m + 63

    10.71

    56y2 − 13y − 3

    10.72

    15x2 − 14x − 16

    10.73

    x2xy + 5x − 5y

    10.74

    x2x + 2xy − 2y

    10.75

    x2 + 15x + 56

    10.76

    y2 + 16y + 28

    10.77

    y2 + 5y − 24

    10.78

    q2 + q − 20

    10.79

    20a2 + 37a − 18

    10.80

    49x2 − 28x − 32

    10.81

    12x2 − 60xxy + 5y

    10.82

    12a2 − 54a − 2ab + 9b

    10.83

    12m2 − 55m + 63

    10.84

    42n2 − 47n + 10

    10.85

    y3 − 8y2 + 9y − 2

    10.86

    3x3 + 2x2 − 3x + 10

    10.87

    y3 − 8y2 + 9y − 2

    10.88

    3x3 + 2x2 − 3x + 10

    10.89
    1. x3
    2. 79
    10.90
    1. y 6
    2. 88
    10.91
    1. 1 x 7 1 x 7
    2. 1 12 10 1 12 10
    10.92
    1. 1 m 9 1 m 9
    2. 1 7 6 1 7 6
    10.93
    1. b 8 b 8
    2. 1 z 6 1 z 6
    10.94
    1. 1 p 8 1 p 8
    2. w 4 w 4
    10.95
    1. 1
    2. 1
    10.96
    1. 1
    2. 1
    10.99
    1. 1
    2. 7x2
    10.100
    1. −23x2
    2. 1
    10.101
    1. 49 81 49 81
    2. y 3 512 y 3 512
    3. p 6 q 6 p 6 q 6
    10.102
    1. 1 64 1 64
    2. 125 m 3 125 m 3
    3. r 4 s 4 r 4 s 4
    10.103

    a 11

    10.104

    b 19

    10.105

    k 2

    10.106

    1 d 1 d

    10.107

    f 12

    10.108

    1 b 10 1 b 10

    10.109

    m 15 n 40 m 15 n 40

    10.110

    t 20 u 14 t 20 u 14

    10.111

    25 b 2 81 c 6 25 b 2 81 c 6

    10.112

    64 p 12 343 q 15 64 p 12 343 q 15

    10.113

    1 y 11 1 y 11

    10.114

    9x5

    10.115

    7x4

    10.116

    16y3

    10.117

    12 y x 2 12 y x 2

    10.118

    9 a 5 9 a 5

    10.119

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

    10.120

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

    10.121

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

    10.122

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

    10.123

    2xy2

    10.124

    −4ab5

    10.125
    1. 1 8 1 8
    2. 1 100 1 100
    10.126
    1. 1 9 1 9
    2. 1 10,000 1 10,000
    10.127
    1. 1 25 1 25
    2. 1 25 1 25
    10.128
    1. 1 4 1 4
    2. 1 4 1 4
    10.129
    1. 2 2
    2. 1 18 1 18
    10.130
    1. 2 2
    2. 1 256 1 256
    10.131

    1 y 7 1 y 7

    10.132

    1 z 8 1 z 8

    10.133
    1. 8 p 8 p
    2. 1 8 p 1 8 p
    3. 1 8 p 1 8 p
    10.134
    1. 11 q 11 q
    2. 1 11 q 1 11 q
    3. 1 11 q 1 11 q
    10.135
    1. x 4 x 4
    2. 1 y 5 1 y 5
    3. 1 z 9 1 z 9
    10.136
    1. a 5 a 5
    2. 1 b 4 1 b 4
    3. 1 c 15 1 c 15
    10.137

    1 p 3 q 3 1 p 3 q 3

    10.138

    1 r 2 s 8 1 r 2 s 8

    10.139

    12 v 5 u 12 v 5 u

    10.140

    30 d 3 c 8 30 d 3 c 8

    10.141

    1 x 4 1 x 4

    10.142

    1 y 4 1 y 4

    10.143

    64 a 8 64 a 8

    10.144

    8 c 12 8 c 12

    10.145

    x 11

    10.146

    y 13

    10.147

    9.6 × 104

    10.148

    4.83 × 104

    10.149

    7.8 × 10−3

    10.150

    1.29 × 10−2

    10.151

    1,300

    10.152

    92,500

    10.153

    0.00012

    10.154

    0.075

    10.155

    0.06

    10.156

    0.009

    10.157

    400,000

    10.158

    20,000

    10.159

    18

    10.160

    16

    10.162

    11

    10.163

    8x2

    10.164

    9y3

    10.165

    3x

    10.166

    5m2

    10.167

    4(x + 3)

    10.168

    6(a + 4)

    10.169

    9(a + 1)

    10.170

    11(x + 1)

    10.171

    11(x − 4)

    10.172

    13(y − 4)

    10.173

    4(y2 + 2y + 3)

    10.174

    6(x2 + 7x − 2)

    10.175

    x(9x + 7)

    10.176

    a(5a − 12)

    10.177

    2x2(x + 6)

    10.178

    3y2(2y − 5)

    10.179

    9y(2y + 7)

    10.180

    8k(4k + 7)

    10.181

    6y(3y2y − 4)

    10.182

    4x(4x2 + 2x − 3)

    10.183

    −5(y + 7)

    10.184

    −8(2z + 7)

    10.185

    −7a(a − 3)

    10.186

    x(6x − 1)

    Section 10.1 Exercises

    1.

    binomial

    3.

    trinomial

    5.

    polynomial

    7.

    monomial

    9.

    5

    11.

    1

    13.

    0

    15.

    15x2

    17.

    −8u

    19.

    5a + 7b

    21.

    −4a −3b

    23.

    16x

    25.

    −17x6

    27.

    12y2 + 4y + 8

    29.

    −3x2 + 17x − 1

    31.

    4a2 − 7a − 11

    33.

    4m2 − 10m + 2

    35.

    11z + 8

    37.

    12s2 − 16s + 9

    39.

    2p3 + p2 + 9p + 10

    41.

    x2 + 3x + 4

    43.

    11w − 66

    45.
    1. 187
    2. 40
    3. 2
    47.
    1. −104
    2. 4
    3. 40
    49.

    19 feet

    51.

    10 mpg

    53.

    Answers will vary.

    Section 10.2 Exercises

    55.

    1,024

    57.

    1 4 1 4

    59.

    0.008

    61.

    625

    63.

    −625

    65.

    −10,000

    67.

    8 27 8 27

    69.

    −0.25

    71.

    x 9

    73.

    a 5

    75.

    314

    77.

    z 6

    79.

    x a+2

    81.

    y a+b

    83.

    u 8

    85.

    y 20

    87.

    1012

    89.

    x 90

    91.

    x 2y

    93.

    5xy

    95.

    25a2

    97.

    −216m3

    99.

    16r2s2

    101.

    256x4y4z4

    103.

    x 14

    105.

    a 36

    107.

    45x3

    109.

    200a5

    111.

    8m18

    113.

    1,000x6y3

    115.

    16a12b8

    117.

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

    119.

    1,024a10

    121.

    25,000p24

    123.

    x 18 y 18

    125.

    144m8n22

    127.

    −60x6

    129.

    72u7

    131.

    4r11

    133.

    36a5b7

    135.

    8x2y5

    137.

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

    139.

    1,679,616

    141.

    Answers will vary.

    143.

    Answers will vary.

    Section 10.3 Exercises

    145.

    4x + 40

    147.

    15r − 360

    149.

    −3m − 33

    151.

    −8z + 40

    153.

    u2 + 5u

    155.

    n3 − 3n2

    157.

    12x2 − 120x

    159.

    −27a2 − 45a

    161.

    24x2 + 6xy

    163.

    55p2 − 25pq

    165.

    3v2 + 30v + 75

    167.

    8n3 − 8n2 + 2n

    169.

    −8y3 − 16y2 + 120y

    171.

    5q5 − 10q4 + 30q3

    173.

    −12z4 − 48z3 + 4z2

    175.

    2y2 − 9y

    177.

    8w − 48

    179.

    x2 + 10x + 24

    181.

    n2 + 9n − 36

    183.

    y2 + 11y + 24

    185.

    a2 + 22a + 96

    187.

    u2 − 14u + 45

    189.

    z2 − 32z + 220

    191.

    x2 + 3x − 28

    193.

    v2 + 7v − 60

    195.

    6n2 + 11n + 5

    197.

    20m2 − 88m − 9

    199.

    16c2 − 1

    201.

    15u2 − 82u + 112

    203.

    2a2 + 5ab + 3b2

    205.

    5x2 − 20xxy + 4y

    207.

    u3 + 7u2 + 14u + 8

    209.

    3a3 + 31a2 + 5a − 50

    211.

    y3 − 16y2 + 69y − 54

    213.

    2x3 − 9x2 − 17x − 6

    215.
    1. 195
    2. 195
    3. Answers will vary.
    217.

    Answers will vary.

    Section 10.4 Exercises

    219.

    46

    221.

    x 9

    223.

    r 4

    225.

    1 y 16 1 y 16

    227.

    1 10 12 1 10 12

    229.

    1 a 8 1 a 8

    231.

    1

    233.

    1

    235.

    −1

    237.
    1. 1
    2. 10
    239.
    1. 1
    2. −27x5
    241.
    1. 1
    2. 15
    243.

    7

    245.

    243 32 243 32

    247.

    m 3 216 m 3 216

    249.

    x 10 y 10 x 10 y 10

    251.

    a 2 9 b 2 a 2 9 b 2

    253.

    x 3

    255.

    u 2

    257.

    1 y 2 1 y 2

    259.

    1

    261.

    1 x 18 1 x 18

    263.

    a 14

    265.

    y 3

    267.

    1 x 10 1 x 10

    269.

    16 r 12 625 s 4 16 r 12 625 s 4

    271.

    1

    273.

    1 r 3 1 r 3

    275.

    3x8

    277.

    8b6

    279.

    −18 x 6 −18 x 6

    281.

    2x

    283.

    5 6 x 6 5 6 x 6

    285.

    6 r 2 s 8 6 r 2 s 8

    287.

    n 6 8 n 6 8

    289.

    4 y 6 5 x 2 4 y 6 5 x 2

    291.

    4 z 3 x 2 y 3 4 z 3 x 2 y 3

    293.

    10 n 2 m 4 10 n 2 m 4

    295.

    5u4v3

    297.
    1. 18n1018n10
    2. 12n1012n10
    3. 45n2045n20
    4. 5 5
    299.
    1. q8q8
    2. q 15 q 15
    301.
    1. z z
    2. 1 z 1 z
    303.

    6y66y6

    305.

    15 c 6 15 c 6

    307.

    3x23x2

    309.

    yz2yz2

    311.

    1,000,000

    313.

    Answers will vary.

    315.

    Answers will vary.

    Section 10.5 Exercises

    317.

    1 64 1 64

    319.

    1 32 1 32

    321.

    1 10 1 10

    323.

    4 9 4 9

    325.

    3 5 3 5

    327.

    3 4 3 4

    329.
    1. 1 64 1 64
    2. 1 64 1 64
    331.
    1. 1 4096 1 4096
    2. 1 4096 1 4096
    333.
    1. 10 3 10 3
    2. 1 30 1 30
    335.
    1. 3 25 3 25
    2. 1 225 1 225
    337.

    1 p 3 1 p 3

    339.

    1 m 5 1 m 5

    341.
    1. 3 q 3 q
    2. 1 3 q 1 3 q
    3. 1 3 q 1 3 q
    343.
    1. 10 k 10 k
    2. 1 10 k 1 10 k
    3. 1 10 k 1 10 k
    345.

    r 3

    347.

    1 q 5 1 q 5

    349.

    1 z 8 1 z 8

    351.

    1 m 1 m

    353.

    1 x 1 x

    355.

    u 2 v 2 u 2 v 2

    357.

    1 a 2 b 4 1 a 2 b 4

    359.

    1 p 5 q 7 1 p 5 q 7

    361.

    21 q 5 p 3 21 q 5 p 3

    363.

    32 a 3 b 32 a 3 b

    365.

    1 q 100 1 q 100

    367.

    1 x 4 1 x 4

    369.

    1 p 6 1 p 6

    371.

    m 6

    373.

    9 q 10 9 q 10

    375.

    n 18 64 n 18 64

    377.

    b 8

    379.

    m 7

    381.

    1 r 3 1 r 3

    383.

    p 3

    385.

    2.8 × 105

    387.

    1.29 × 106

    389.

    4.1 × 10−2

    391.

    1.03 × 10−5

    393.

    6.85 × 109

    395.

    5.7 × 10−9

    397.

    830

    399.

    16,000,000,000

    401.

    0.028

    403.

    0.0000000615

    405.

    $15,000,000,000,000

    407.

    0.00001

    409.

    0.003

    411.

    0.00000735

    413.

    20,000,000

    415.

    50,000,000

    417.
    1. 1.25 × 10−4
    2. 8,000
    419.

    11,441,304,000

    421.

    Answers will vary.

    Section 10.6 Exercises

    423.

    15

    425.

    25

    427.

    4

    429.

    5

    431.

    3x

    433.

    12p3

    435.

    2a

    437.

    10y

    439.

    5x3

    441.

    7b2

    443.

    5(y + 3)

    445.

    4(b − 5)

    447.

    7(x − 1)

    449.

    3(n2 + 7n + 4)

    451.

    6(q2 + 5q + 7)

    453.

    c(9c + 22)

    455.

    x(17x + 7)

    457.

    q(4q + 7)

    459.

    3r(r + 9)

    461.

    10u(3u − 1)

    463.

    b(a + 8)

    465.

    11y(5 − y3)

    467.

    15c2(3c − 1)

    469.

    6c(c2d2)

    471.

    24x2(2x + 3)

    473.

    18a3(8a3 + 5)

    475.

    10(y2 + 5y + 4)

    477.

    12(u2 − 3u − 9)

    479.

    5p2(p2 − 4p − 3)

    481.

    8c3(c2 + 5c − 7)

    483.

    −7(p + 12)

    485.

    −6b(3b + 11)

    487.

    −8a2(a − 4)

    489.

    −9b3(b2 − 7)

    491.

    −4(4t2 − 20t − 1)

    493.

    Answers will vary.

    Review Exercises

    494.

    trinomial

    496.

    binomial

    498.

    2

    500.

    0

    502.

    15p

    504.

    −3n5

    506.

    10a2 + 4a − 1

    508.

    6y2 − 3y + 3

    510.

    8q3 + q2 + 6q − 29

    512.

    995

    514.

    2,955

    516.

    −163

    518.

    64 feet

    520.

    216

    522.

    0.25

    524.

    p 13

    526.

    a 6

    528.

    y 12

    530.

    310

    532.

    64n2

    534.

    256a8b8

    536.

    27a15

    538.

    x 21

    540.

    −54p5

    542.

    56x3y11

    544.

    70 − 7x

    546.

    −625y4 + 5y

    548.

    a2 + 7a + 10

    550.

    6x2 − 19x − 7

    552.

    n2 + 9n + 8

    554.

    5u2 + 37u − 24

    556.

    p2 + 11p + 28

    558.

    27c2 − 3c − 4

    560.

    x3 − 2x2 − 24x − 21

    562.

    m3m2 − 72m − 180

    564.

    26 or 64

    566.

    1 n 9 1 n 9

    568.

    1

    570.

    1

    572.

    9 25 9 25

    574.

    125 m 3 n 3 125 m 3 n 3

    576.

    a 2

    578.

    1 x 40 1 x 40

    580.

    1 n 1 n

    582.

    9p9

    584.

    3 y 4 3 y 4

    586.

    4 a 5 b 2 4 a 5 b 2

    588.

    4 m 9 n 4 4 m 9 n 4

    590.

    1 36 1 36

    592.

    5 16 5 16

    594.

    x 6

    596.

    1 u 3 v 5 1 u 3 v 5

    598.

    k 6

    600.

    b 10

    602.

    5.3 × 106

    604.

    9.7 × 10−2 millimeter

    606.

    29,000

    608.

    0.375

    610.

    6,000

    612.

    30,000,000,000

    614.

    5

    616.

    4x2

    618.

    8(2u − 3)

    620.

    6p(p + 1)

    622.

    −9a3(a2 + 1)

    624.

    5(y2 − 11y + 9)

    Practice Test

    626.
    1. trinomial
    2. 4
    628.

    6x2 − 3x + 11

    630.

    n 5

    632.

    −48x5y9

    634.

    s2 + 17s + 72

    636.

    55a2 − 41a + 6

    638.

    24a2 + 34ab − 45b2

    640.

    x 14

    642.

    4 r s 6 4 r s 6

    644.

    3y2 − 7x

    646.

    1 8 y 3 1 8 y 3

    648.

    x 9

    650.

    −6x(x + 5)

    652.

    0.000525

    654.

    300,000 300,000


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