Prealgebra 2e

# Chapter 10

Prealgebra 2eChapter 10

## 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. $25642564$
2. $0.44890.4489$
10.24
1. $81258125$
2. $0.0161290.016129$
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. x28
2. 732
10.38
1. x54
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. y6
2. 88
10.91
1. $1x71x7$
2. $1121011210$
10.92
1. $1m91m9$
2. $176176$
10.93
1. $b8b8$
2. $1z61z6$
10.94
1. $1p81p8$
2. $w4w4$
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. $49814981$
2. $y3512y3512$
3. $p6q6p6q6$
10.102
1. $164164$
2. $−125m3−125m3$
3. $r4s4r4s4$
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. $1818$
2. $11001100$
10.126
1. $1919$
2. $110,000110,000$
10.127
1. $125125$
2. $−125−125$
10.128
1. $1414$
2. $−14−14$
10.129
1. $22$
2. $118118$
10.130
1. $22$
2. $12561256$
10.131

$1 y 7 1 y 7$

10.132

$1 z 8 1 z 8$

10.133
1. $8p8p$
2. $18p18p$
3. $−18p−18p$
10.134
1. $11q11q$
2. $111q111q$
3. $−111q−111q$
10.135
1. $x4x4$
2. $1y51y5$
3. $1z91z9$
10.136
1. $a5a5$
2. $1b41b4$
3. $1c151c15$
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.

## 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.

143.

## 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.

## 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. $55$
299.
1. $q8q8$
2. $q15q15$
301.
1. $zz$
2. $1z1z$
303.

$6y66y6$

305.

$15 c 6 15 c 6$

307.

$3x23x2$

309.

$−yz2−yz2$

311.

1,000,000

313.

315.

## 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. $164164$
2. $−164−164$
331.
1. $1409614096$
2. $−14096−14096$
333.
1. $103103$
2. $130130$
335.
1. $325325$
2. $12251225$
337.

$1 p 3 1 p 3$

339.

$1 m 5 1 m 5$

341.
1. $3q3q$
2. $13q13q$
3. $−13q−13q$
343.
1. $10k10k$
2. $110k110k$
3. $−110k−110k$
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.

## 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.

## 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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