57a. (4 + 9n2)(2 + 3n)(2 - 3n) b. They are squares of
square terms, c. Answers may vary. Sample:
16X4 - 1 59. H 61a. c = 190 - 2p b. graph of a line
through (0, 200), (1, 198), (2, 196), (3, 194), (4, 192),
(5, 190)
- ( 6 x + 7)(3x - 2) 63. (2x + 3)(4x + 3)
- (4x — 7)(3x — 5) 65. 2 66. 3m 67. 4b 2
Lesson 8-8 pp. 5 29-533
Go t It? 1a. (2f 2 + 5 ) ( 4 f + 7) b. Answers may vary.
Sample: In Lesson 8 - 6 , you rewrote the middle term as the
sum of two terms and then factored by grouping. In this
problem, there were already two middle terms. - 3b (b 2 + 2)(2b + 3) 3. Answers may vary. Sample:
2x, 5x + 2, and 6 x + 1
Lesso n Ch eck 1. (4r 2 + 3)(5r+ 2) - (3d 2 - 5 )(2cf + 1) 3. 6(2x 2 + 3)(2x+5)
- Answers may vary. Sample: 4x, 3x + 1, and 3x + 2
- No; the polynomial is a perfect square. 6. Yes; w h e n
you write 23w as 20 w + 3 w th e resulting two groups of
terms have the same factor, w+ 5. 7. Yes; two groups of
terms have the same factor, 41— 7. 8. No; when you
factor out the GCF from each pair of terms, there is no
common factor.
Ex e r c i se s 9. 2z 2, 3 11. 2 r2, -5 13. (5g 2 + 1 )(3q + 8 )
15. (7z 2 + 8)(2 z-5 ) 17. (2m +1)(2m -1)(2m + 3)
19. (4v 2 -5)(5v+ 6) 21. (4y 2 -3)(3y + 1)
23. w(w2 + 6 )(3 w - 2) 25. 3q(q + 2)(q - 2)(2q + 1)
27. 2(d 2 + 4 )(2 d - 3) 29. Answers may vary. Sample:
4c, c + 8 , and c+ 5 31. 9f(f- 8 )(f- 2)
33. 8 (m 2 + 5)(m + 4) 35. The factorization is correct,
but it is not complete. The GCF of all the terms is 4x, not 4.
4x 4 + 12x 3 + 8 x 2 + 24x = 4x(x 3 + 3x 2 + 2x + 6 ) =
4x [x2(x + 3) + 2(x + 3)] = 4x(x 2 + 2 )(x + 3)
37. Answers may vary. Sample: Split the expression into
three binomials. Find the GCF of each binomial, then
factor again. 39. Answers may vary. Sample:
30x3 + 36x2 + 40x + 48 = 2 (3x 2 + 4)(5x + 6 ) - (y + 2)(y — 2 ) ( y + 1 1 ) 4 3. ( 6 g 3 - 7b 2 )(5g 2 + 4b)
- (2 3 + 2°)(2 2 + 2 1 + 2°); 9(7) 47. D 49. B
51. 5r(2r 2 + 1 )(r + 3) 52. (m + 6)2 53. ( 8 x - 9)2
54. (7p + 2)(7p - 2) 55. not a function
56. function 57. function
Chapter Review pp. 535-538- binomial 2. polynomial 3. monomial 4. perfect-
square trinomial 5. degree of the monomial - -9r2 + 11 r + 3; quadratic trinomial 7. b3 + b2 + 3;
cubic trinomial 8. 8t2 + 3; quadratic binomial - 4 n 5 + n; fifth degree binomial 10. 6 x+ 8 ; linear
binomial 11. p 3g 3; sixth degree monomial 12. v 3 + 5
13. 14s4 - 4s2 + 9s + 7 14. 9b3 - 3b + 3
15. 7z3 - 2z2 - 16 16. -20k2 + 15/c
17. 36m3 + 8m2 - 24m 18. 6g3 - 48g2
19. 3d3 + 18d2 20. -8n4 - 10 n 3 + 18n2
21. -2q3 + 8g2 + 11g 22. 4p(3p3 + 4p2 + 2)
23. 3b(b3 - 3b + 2) 24. 90(5^ - 7c2 + 3)
25. 4g(g + 2) 26. 3(f4-2 f3-3t + 4)
27. 3b3(10b2 - 2b - 5) 28. 30; if the GCF of p and q
is 5, then the GCF of 6 p and 6 g is 6(5) = 30.
29. w2 + 13w + 12 30. 10s2 - 7 s - 12
31. 9r2 - 12r + 4 32. 6 g2 -41g-56
33. 21g2 + 62g + 16 34. 12n4 + 20n3 + 15n + 25
35. t2 + 6 t - 27 36. 36c2 + 60c + 25
37. 49b2 - 9 38. 3y2 — 1 1y — 42
39. 32a2 - 44a - 21 40. 16b2 - 9 - (3x + 5)(x + 7); 3x2 + 26x + 35
- (g - 7)(g + 2) 43. (2n - 1 )(n + 2)
- 2(3k - 2€){k - €) 45. (p + 6)(p + 2)
- (r + 10 )(r - 4) 47. (2m + n)(3m + 11 n)
- (t + 2)(t - 15) 49. (2g — 1 )(g — 17)
50. 3(x + 2)(x - 1) 51. (d -3 )(d - 15)
52. {w + 3)(w - 18) 53. 7(3z - 7)(z - 1)
54. -2 (b - 7)(b + 5) 55. (x + 2)(x + 19)
56. (5v + 8)(2v - 1) 5 7. 5(g + 2)(g + 1) 58. Answers
may vary. Sample: If the expression is factorable then there
must be factors of 18 whose sum is b = 15. The factors of 18
are 1 and 18, 2 and 9, 3 and 6. None of these have a sum
equal to 15, so the expression is not factorable. 59. (s - 10)2
60. (4g + 7)2 61. (r + 8 )(r - 8 ) 62. (3z + 4)(3z - 4)
63. (5m + 8)2 64. (7n + 2)(7n - 2)
65. (g + 15)(g - 15) 66. (3p - 7)2 67. (6b - 1 )2
68. (w + 12)2 69. 8(2v + 1)(2v- 1)