Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis

Chapter 7

Be Prepared

7.1

$2 \cdot 2 \cdot 2 \cdot 7$

7.2

72

7.3

$- 18 a - 33$

7.4

$x^{2} + 9 x + 20$

7.5

ⓐ −15 ⓑ −3

7.6

ⓐ −54 ⓑ 54

7.7

7.8

$15 p^{2}$

7.9

$6 y^{2} + 23 y + 20$

7.10

$12 x^{2} + 8 x + 9$

7.11

$144 x^{2}$

7.12

$m^{2} - 8 m + 16$

7.13

$p^{2} - 18 p + 81$

7.14

$k^{2} - 9$

7.15

$(y - 6) (y + 4)$

7.16

$(3 t + 2) (t + 5)$

7.17

${(6 p - 5)}^{2}$

7.18

$5 (x - 4) (x + 4)$

7.19

$y = \frac{3}{5}$

7.20

$a = 0$

7.21

$12 x^{2} - 2 x$

7.22

$n (n - 11) (n + 2)$

Try It

7.1

16

7.2

2

7.3

$6 x^{2}$

7.4

$8 y^{2}$

7.5

$2 a b$

7.6

$3 m^{3} n$

7.7

$5 m^{2}$

7.8

$7 x$

7.9

$6 (a + 4)$

7.10

$2 (b + 7)$

7.11

$14 (x + 1)$

7.12

$12 (p + 1)$

7.13

$18 (u - 2)$

7.14

$30 (y - 2)$

7.15

$5 (x^{2} - 5 x + 3)$

7.16

$3 (y^{2} - 4 y + 9)$

7.17

$2 x^{2} (x + 6)$

7.18

$3 y^{2} (2 y - 5)$

7.19

$2 x (10 x^{2} - 5 x + 7)$

7.20

$4 y (6 y^{2} - 3 y - 5)$

7.21

$3 y^{2} (3 x + 2 x^{2} + 7 y)$

7.22

$3 p (p^{2} - 2 p q + 3 q^{3})$

7.23

$−16 (z + 4)$

7.24

$−9 (y + 3)$

7.25

$−4 b (b - 4)$

7.26

$−7 a (a - 3)$

7.27

$(m + 3) (4 m - 7)$

7.28

$(n - 4) (8 n + 5)$

7.29

$(x + 8) (y + 3)$

7.30

$(a + 7) (b + 8)$

7.31

$(x - 5) (x + 2)$

7.32

$(y + 4) (y - 7)$

7.33

$(x + 2) (x + 4)$

7.34

$(y + 3) (y + 5)$

7.35

$(q + 4) (q + 6)$

7.36

$(t + 2) (t + 12)$

7.37

$(x + 4) (x + 15)$

7.38

$(v + 3) (v + 20)$

7.39

$(u - 3) (u - 6)$

7.40

$(y - 7) (y - 9)$

7.41

$(h - 2) (h + 6)$

7.42

$(k - 4) (k + 5)$

7.43

$(x + 2) (x - 6)$

7.44

$(y + 4) (y - 5)$

7.45

$(r + 5) (r - 8)$

7.46

$(s + 2) (s - 5)$

7.47

prime

7.48

prime

7.49

$(m + 3) (m + 6)$

7.50

$(n - 3) (n - 4)$

7.51

$(u + 4 v) (u + 7 v)$

7.52

$(x + 6 y) (x + 7 y)$

7.53

$(a - b) (a - 10 b)$

7.54

$(m - n) (m - 12 n)$

7.55

prime

7.56

prime

7.57

ⓐ no method ⓑ undo using FOIL ⓒ factor with grouping

7.58

ⓐ factor using grouping ⓑ no method ⓒ undo using FOIL

7.59

$4 (m + 1) (m - 2)$

7.60

$5 (k + 2) (k - 5)$

7.61

$3 (r - 1) (r - 2)$

7.62

$2 (t - 2) (t - 3)$

7.63

$5 x (x - 1) (x + 4)$

7.64

$6 y (y - 2) (y + 5)$

7.65

$(a + 1) (2 a + 3)$

7.66

$(b + 1) (4 b + 1)$

7.67

$(2 x - 3) (4 x - 1)$

7.68

$(2 y - 7) (5 y - 1)$

7.69

$(a - 1) (8 a + 5)$

7.70

$(2 b + 3) (3 b - 5)$

7.71

$(3 x + 2) (6 x - 5)$

7.72

$(3 y + 1) (10 y - 21)$

7.73

$5 n (n - 4) (3 n - 5)$

7.74

$8 q (q + 6) (7 q - 2)$

7.75

$(x + 2) (6 x + 1)$

7.76

$(2 y + 1) (2 y + 3)$

7.77

$(4 h + 5) (5 h - 3)$

7.78

$(g + 4) (6 g - 5)$

7.79

$(2 t + 5) (5 t - 3)$

7.80

$(u + 1) (3 u + 5)$

7.81

$4 (2 x - 3) (2 x - 1)$

7.82

$3 (3 w - 2) (2 w - 3)$

7.83

${(2 x + 3)}^{2}$

7.84

${(3 y + 4)}^{2}$

7.85

${(8 y - 5)}^{2}$

7.86

${(4 z - 9)}^{2}$

7.87

${(7 x + 6 y)}^{2}$

7.88

${(8 m + 7 n)}^{2}$

7.89

$(8 r + 3 s) (2 r + 3 s)$

7.90

$(3 u + 4) (3 u + 25)$

7.91

$2 y {(2 x - 3)}^{2}$

7.92

$3 q {(3 p + 5)}^{2}$

7.93

$(h - 9) (h + 9)$

7.94

$(k - 11) (k + 11)$

7.95

$(m - 1) (m + 1)$

7.96

$(9 y - 1) (9 y + 1)$

7.97

$(14 m - 5 n) (14 m + 5 n)$

7.98

$9 (4 p - q) (4 p + q)$

7.99

$(12 - x) (12 + x)$

7.100

$(13 - p) (13 + p)$

7.101

$(a^{2} + b^{2}) (a + b) (a - b)$

7.102

$(x^{2} + 4) (x + 2) (x - 2)$

7.103

$7 x (y - 5) (y + 5)$

7.104

$5 b (3 a - 4) (3 a + 4)$

7.105

$8 (a^{2} + 25)$

7.106

$9 (4 y^{2} + 9)$

7.107

$(x + 3) (x^{2} - 3 x + 9)$

7.108

$(y + 2) (y^{2} - 2 y + 4)$

7.109

$(u - 5) (u^{2} + 5 u + 25)$

7.110

$(v - 7) (v^{2} + 7 v + 49)$

7.111

$(4 - 3 x) (16 + 12 x + 9 x^{2})$

7.112

$(3 - 2 y) (9 + 6 y + 4 y^{2})$

7.113

$(2 x - 3 y) (4 x^{2} + 6 x y + 9 y^{2})$

7.114

$125 (2 m - n) (4 m^{2} + 8 m n + n^{2})$

7.115

$4 (5 p + q) (25 p^{2} - 5 p q + q^{2})$

7.116

$2 (6 c + 7 d) (36 c^{2} - 42 c d + 49 d^{2})$

7.117

$3 a^{3} (a + 6)$

7.118

$9 b^{5} (5 b + 3)$

7.119

$(5 a - 6) (2 a - 1)$

7.120

$(2 x - 3) (4 x - 3)$

7.121

$x (x^{2} + 36)$

7.122

$3 (9 y^{2} + 16)$

7.123

$4 x (2 x - 3) (2 x + 3)$

7.124

$3 (3 y - 4) (3 y + 4)$

7.125

${(2 x + 5 y)}^{2}$

7.126

${(3 m + 7 n)}^{2}$

7.127

$8 (y - 1) (y + 3)$

7.128

$5 (u - 9) (u + 6)$

7.129

$2 (5 m + 6) (25 m^{2} - 30 m + 36)$

7.130

$3 (3 q + 4) (9 q^{2} - 12 q + 16)$

7.131

$4 (a^{2} + 4) (a - 2) (a + 2)$

7.132

$7 (y^{2} + 1) (y - 1) (y + 1)$

7.133

$6 (x + b) (x - 2 c)$

7.134

$2 (4 x - 1) (2 x + 3 y)$

7.135

$4 (p - 1) (p - 3)$

7.136

$3 (q - 2) (2 q + 1)$

7.137

$x = 3, x = −5$

7.138

$y = 6, y = −9$

7.139

$m = \frac{2}{3}, m = - \frac{1}{2}$

7.140

$p = - \frac{3}{4}, p = \frac{3}{4}$

7.141

$u = 0, u = \frac{1}{5}$

7.142

$w = 0, w = - \frac{3}{2}$

7.143

$x = −1$

7.144

$v = 2$

7.145

$x = 4, x = −3$

7.146

$b = −2, b = −7$

7.147

$c = 2, c = \frac{4}{3}$

7.148

$d = 3, d = - \frac{1}{2}$

7.149

$a = 0, a = −1$

7.150

$b = 0, b = - \frac{1}{3}$

7.151

$p = \frac{7}{5}, p = - \frac{7}{5}$

7.152

$x = \frac{11}{6}, x = - \frac{11}{6}$

7.153

$m = 1, m = \frac{3}{2}$

7.154

$k = 3, k = −3$

7.155

$x = 0, x = \frac{3}{2}$

7.156

$y = 0, y = \frac{1}{4}$

7.157

$a = - \frac{5}{2}, a = \frac{2}{3}$

7.158

$b = −2, b = - \frac{1}{20}$

7.159

$−15, −16 and 15, 16$

7.160

$−21, −20 and 20, 21$

7.161

$5$ feet and $6$ feet

7.162

$12$ feet and $15$ feet

7.163

$5$ feet and $12$ feet

7.164

$24$ feet and $25$ feet

Section 7.1 Exercises

1.

2

3.

18

5.

10

7.

$x$

9.

$8 w^{2}$

11.

$2 p q$

13.

$6 m^{2} n^{3}$

15.

$2 a$

17.

$5 x^{3}$

19.

$4 (x + 5)$

21.

$3 (2 m + 3)$

23.

$9 (q + 1)$

25.

$8 (m - 1)$

27.

$9 (n - 7)$

29.

$3 (x^{2} + 2 x - 3)$

31.

$2 (4 p^{2} + 2 p + 1)$

33.

$8 y^{2} (y + 2)$

35.

$5 x (x^{2} - 3 x + 4)$

37.

$6 y^{2} (2 x + 3 x^{2} - 5 y)$

39.

$−2 (x + 2)$

41.

$(x + 1) (5 x + 3)$

43.

$(b - 2) (3 b - 13)$

45.

$(y + 3) (x + 2)$

47.

$(u + 2) (v - 9)$

49.

$(b - 4) (b + 5)$

51.

$(p - 9) (p + 4)$

53.

$−10 (2 x + 1)$

55.

$(x^{2} + 2) (3 x - 7)$

57.

$(x + y) (x + 5)$

59.

$w (w - 6)$

61.

Answers will vary.

Section 7.2 Exercises

63.

$(x + 1) (x + 3)$

65.

$(m + 1) (m + 11)$

67.

$(a + 4) (a + 5)$

69.

$(p + 5) (p + 6)$

71.

$(n + 3) (n + 16)$

73.

$(a + 5) (a + 20)$

75.

$(x - 2) (x - 6)$

77.

$(y - 3) (y - 15)$

79.

$(x - 1) (x - 7)$

81.

$(p - 1) (p + 6)$

83.

$(y + 1) (y - 7)$

85.

$(x - 4) (x + 3)$

87.

$(a - 7) (a + 4)$

89.

$(w - 9) (w + 4)$

91.

prime

93.

$(x - 4) (x - 2)$

95.

$(x - 12) (x + 1)$

97.

$(p + q) (p + 2 q)$

99.

$(r + 3 s) (r + 12 s)$

101.

$(m - 2 n) (m - 10 n)$

103.

$(x + 8 y) (x - 10 y)$

105.

$(m + n) (m - 65 n)$

107.

$(a + 8 b) (a - 3 b)$

109.

prime

111.

prime

113.

$(u - 6) (u - 6)$

115.

$(x + 2) (x - 16)$

117.

$(r - 4 s) (r - 16 s)$

119.

$(k + 4) (k + 30)$

121.

prime

123.

$(m + 8 n) (m - 7 n)$

125.

$(u - 15 v) (u - 2 v)$

127.

prime

129.

$(x + 8) (x - 7)$

131.

Answers may vary

133.

Answers may vary

Section 7.3 Exercises

135.

ⓐ factor the GCF, binomial ⓑ Undo FOIL ⓒ factor by grouping

137.

ⓐ undo FOIL ⓑ factor by grouping ⓒ factor the GCF, binomial

139.

$5 (x + 1) (x + 6)$

141.

$2 (z - 4) (z + 3)$

143.

$7 (v - 1) (v - 8)$

145.

$p (p - 10) (p + 2)$

147.

$3 m (m - 5) (m - 2)$

149.

$5 x^{2} (x - 3) (x + 5)$

151.

$(2 t + 5) (t + 1)$

153.

$(11 x + 1) (x + 3)$

155.

$(4 w - 1) (w - 1)$

157.

$(3 p - 2) (2 p - 5)$

159.

$(4 q + 1) (q - 2)$

161.

$(4 p - 3) (p + 5)$

163.

$16 (x - 1) (x - 1)$

165.

$10 q (3 q + 2) (q + 4)$

167.

$(5 n + 1) (n + 4)$

169.

$(3 z + 1) (3 z + 4)$

171.

$(2 k - 3) (2 k - 5)$

173.

$(5 s - 4) (s - 1)$

175.

$(3 y + 5) (2 y - 3)$

177.

$(2 n + 3) (n - 15)$

179.

prime

181.

$10 (6 y - 1) (y + 5)$

183.

$3 z (8 z + 3) (2 z - 5)$

185.

$8 (2 s + 3) (s + 1)$

187.

$12 (4 y - 3) (y + 1)$

189.

$(4 y - 7) (3 y - 2)$

191.

$(a - 5) (a + 4)$

193.

$(2 n - 1) (3 n + 4)$

195.

prime

197.

$13 (z^{2} + 3 z - 2)$

199.

$(x + 7) (x - 4)$

201.

$3 p (p + 7)$

203.

$6 (r + 2) (r + 3)$

205.

$4 (2 n + 1) (3 n + 1)$

207.

$(x + 6) (x - 4)$

209.

$−16 (t - 6) (t + 1)$

211.

Answers may vary.

213.

Answers may vary.

Section 7.4 Exercises

215.

${(4 y + 3)}^{2}$

217.

${(6 s + 7)}^{2}$

219.

${(10 x - 1)}^{2}$

221.

${(5 n - 12)}^{2}$

223.

${(7 x - 2 y)}^{2}$

225.

$(5 n + 4) (5 n + 1)$

227.

$(8 m - 1)^{2}$

229.

$10 {(k + 4)}^{2}$

231.

$3 u {(5 u - v)}^{2}$

233.

$(x - 4) (x + 4)$

235.

$(5 v - 1) (5 v + 1)$

237.

$(11 x - 12 y) (11 x + 12 y)$

239.

$(13 c - 6 d) (13 c + 6 d)$

241.

$(2 - 7 x) (2 + 7 x)$

243.

$(2 z - 1) (2 z + 1) (4 z^{2} + 1)$

245.

$5 (q - 3) (q + 3)$

247.

$6 (4 p^{2} + 9)$

249.

$(x + 5) (x^{2} - 5 x + 25)$

251.

$(z - 3) (z^{2} + 3 z + 9)$

253.

$(2 - 7 t) (4 + 14 t + 49 t^{2})$

255.

$(2 y - 5 z) (4 y^{2} + 10 y z + 25 z^{2})$

257.

$7 (k + 2) (k^{2} - 2 k + 4)$

259.

$2 (1 - 2 y) (1 + 2 y + 4 y^{2})$

261.

$(8 a - 5) (8 a + 5)$

263.

$3 (3 q - 1) (3 q + 1)$

265.

${(4 x - 9)}^{2}$

267.

$2 (4 p^{2} + 1)$

269.

$(5 - 2 y) (25 + 10 y + 4 y^{2})$

271.

$5 {(3 n + 2)}^{2}$

273.

${(2 w + 15)}^{2}$

275.

Answers may vary.

277.

Answers may vary.

Section 7.5 Exercises

279.

$5 x^{3} (2 x + 7)$

281.

$(y - 3) (y + 13)$

283.

$(2 n - 1) (n + 7)$

285.

$a^{3} (a^{2} + 9)$

287.

$(11 r - s) (11 r + s)$

289.

$8 (m - 2) (m + 2)$

291.

${(5 w - 6)}^{2}$

293.

${(m + 7 n)}^{2}$

295.

$7 (b + 3) (b - 2)$

297.

$3 (x - 3) (x^{2} + 3 x + 9)$

299.

$(k - 2) (k + 2) (k^{2} + 4)$

301.

$3 (5 p + 4) (q - 1)$

303.

$4 (x + 3) (x + 7)$

305.

$u^{2} (u + 1) (u^{2} - u + 1)$

307.

prime

309.

$10 (m - 5) (m + 5) (m^{2} + 25)$

311.

ⓐ $−16 (t^{2} - 5)$ ⓑ $−8 (2 t + 5) (t - 2)$

313.

Answer may vary.

Section 7.6 Exercises

315.

$x = 3, x = −7$

317.

$a = 10 / 3, a = 7 / 2$

319.

$m = 0, m = 5 / 12$

321.

$y = 3$

323.

$x = 1 / 2$

325.

$x = −3, x = −4$

327.

$a = −4 / 5, a = 6$

329.

$m = 5 / 4, m = 3$

331.

$a = −1, a = 0$

333.

$m = 12 / 7, m = −12 / 7$

335.

$y = −1, y = 6$

337.

$x = 3 / 2, x = −1$

339.

$p = 0, p = ¾$

341.

$x = 3 / 2$

343.

$7 and 8; - 8 and −7$

345.

$4 feet and 7 feet$

347.

$6 feet and 8 feet$

349.

$x = −8, x = 3$

351.

$p = −1, p = −11$

353.

$m = −2, m = 8$

355.

$a = 0, a = −6, a = 7$

357.

$10 and 11; - 11 and −10$

359.

10 feet

361.

Answers may vary.

Review Exercises

363.

6

365.

$15$

367.

$6 (4 x - 7)$

369.

$3 m^{2} (5 m^{2} + 2 n)$

371.

$(a + b) (x - y)$

373.

$(x - 3) (x + 7)$

375.

$(m^{2} + 1) (m + 1)$

377.

$(u + 8) (u + 9)$

379.

$(k - 6) (k - 10)$

381.

$(y + 7) (y - 1)$

383.

$(s - 4) (s + 2)$

385.

$(x + 5 y) (x + 7 y)$

387.

$(a + 7 b) (a - 3 b)$

389.

Undo FOIL

391.

Factor the GCF

393.

$6 (x + 2) (x + 5)$

395.

$3 n^{2} (n - 8) (n + 4)$

397.

$(x + 4) (2 x + 1)$

399.

$(3 a - 1) (6 a - 1)$

401.

$(5 p + 4) (3 p - 2)$

403.

$(5 s - 2) (8 s + 3)$

405.

$3 (x + 4) (x - 3)$

407.

$5 (4 y + 1) (3 y - 5)$

409.

${(5 x + 3)}^{2}$

411.

${(6 a - 7 b)}^{2}$

413.

$10 {(2 x + 9)}^{2}$

415.

$2 y {(y - 4)}^{2}$

417.

$(9 r - 5) (9 r + 5)$

419.

$(13 m + n) (13 m - n)$

421.

$(5 p - 1) (5 p + 1)$

423.

$(3 + 11 y) (3 - 11 y)$

425.

$5 (2 x - 5) (2 x + 5)$

427.

$u (7 u + 3) (7 u - 3)$

429.

$(a - 5) (a^{2} + 5 a + 25)$

431.

$2 (m + 3) (m^{2} - 3 m + 9)$

433.

$4 x^{2} (6 x + 11)$

435.

${(4 n - 7 m)}^{2}$

437.

$(r + 6) (5 r - 8)$

439.

$(n^{2} + 9) (n + 3) (n - 3)$

441.

$5 (x - 3) (x + 4)$

443.

$(m + 5) (m^{2} - 5 m + 25)$

445.

$a = 3, a = −7$

447.

$m = 0 m = –6 m = \frac{5}{2}$

449.

$x = −4, x = −5$

451.

$p = - \frac{5}{2}, p = 8$

453.

$m = \frac{5}{12}, m = - \frac{5}{12}$

455.

$−21 and −22; 21 and 22$

Practice Test

457.

$14 (y - 3)$

459.

$40 a^{2} (2 + 3 a)$

461.

$(x + 7) (x + 6)$

463.

$3 a (a - 6) (a + 4)$

465.

$5 (n + 3)^{2}$

467.

$(x - 8) (y + 7)$

469.

${(3 s - 2)}^{2}$

471.

$(10 - a) (10 + a)$

473.

$3 (x + 5 y) (x - 5 y)$

475.

$(a - 3) (b - 2)$

477.

$(4 m + 1) (2 m + 5)$

479.

$y = −11, y = 12$

481.

$b = 1, b = −1$

483.

$n = - \frac{7}{4}, n = −3$

485.

$12 and 13; - 13 and −12$