Factoring by Grouping pages 499–501 Exercises ALGEBRA 1 LESSON 9-8 pages 499–501  Exercises 1. 2m2; 3 2. 5p2; 2 3. 2z2; –5 4. 3n2; 1 5. (2n2 + 1)(3n + 4) 6. (7t 2 + 8)(2t + 3) 7. (3t + 1)(3t – 1)(3t + 5) 8. (y2 + 1)(13y – 8) 9. (5x2 + 1)(9x + 4) 10. (2w2 – 3)(5w + 8) 11. 2(2v2 + 1)(3v – 8) 12. q(q 2 + 4)(7q – 4) 13. 2(m2 + 2)(10m – 9) 14. 2x(x + 1)(x – 1)(3x + 2) 15. 2(2y2 + 5)(3y – 5) 16. 3(c2 + 2)(3c – 4) 17. (6p + 5)(2p + 1) 18. (4t + 3)2 19. (6n – 1)(3n + 10) 20. (3w – 5)(3w – 4) 21. 2(6m – 1)(2m + 1) 22. (12v – 7)(3v + 1) 23. (3x – 2)(2x + 5) 24. (4v – 1)(5v – 9) 25. (7q + 2)(9q – 10) 26. m, (3m + 1), and (m + 2) 27. 5k, (k + 2), and (k + 4) 28. 7h(h – 6)(h + 1) 29. 2(10t 2 – 11)(3t – 10) 30. 8(d 2 + 3)(d + 2) 31. 4(3x – 7y)(x + 2y) 32. 9r (3r – 1)(2r – 1) 33. 10(5k2 + 6)(3k + 7) 34. a. (7x2 + 9)(4x – 1) b. (4x – 1)(7x2 + 9) c. Answers may vary. Sample: The factorings are equivalent; but the factors may appear in a different order. 9-8

40. Answers may vary. Sample: 30x2 + 36x + 40x + 48; 2(3x + 4)(5x + 6) Factoring by Grouping ALGEBRA 1 LESSON 9-8 35. (7w 2 – 4)(2w + 7) 36. (2m2 – 1)(m – 16) 37. 2(2t 2 + 3)(11t – 1) 38. (x2 – 2)(25x – 1) 39. 2w, (6w + 5), and (7w + 1) 40. Answers may vary. Sample: 30x2 + 36x + 40x + 48; 2(3x + 4)(5x + 6) 41. Answers may vary. Sample: Split the expression into two groups. Remove the GCF from each group, and then factor again. 42. (6m3 – 7n2)(5m2 + 4n) 43. (x2 + y)(p + q5) 44. (h + 2)(h – 2)(h + 11) 45. (w 2 + 3)(w 2 – 3)(w + 1)(w – 1) 46. a. 2 x(x + 3)2 b. x + 3 47. (23 + 20)(22 + 21 + 20); (9)(7) 48. (24 + 22 + 20) (21 + 20); (21)(3) 49. Answers may vary. Samples are given. a. length = 2x + 4; width = x; height = x + 4 b. 2x3 + 12x2 + 16x 50. C 51. H 52. [2] 9a4 – 54a3 – 2a + 12 = 9a3(a – 6) – 2(a – 6) = (9a3 – 2)(a – 6) [1] appropriate methods with one computational error 9-8

solutions on the line y = –4x+ 25 84. (7, 2) Factoring by Grouping ALGEBRA 1 LESSON 9-8 58. (m + 8)(m – 8) 59. 4(g + 5)2 60. (2d + 5)(2d – 5) 61. 5(n + 3)(n – 3) 62. (5q + 4)2 63. b4 64. x2 65. t 15 66. c35d 7 67. 8y3 68. 1 69. 70. 81w8v12 71. 1.6  1021 1 x11 72. 9  1012 73. 4.9  10–11 74. 3.2  1036 75. 2.809  105 76. 6.561  10–5 77. 6.859  1024 78. 6.25  104 79. (1, 5) 80. (4, –8) 81. (0.5, 5) 82. (2, –30) 83. infinitely many solutions on the line y = –4x+ 25 84. (7, 2) 53. [4] 96x3 + 48x2 + 6x = 6x(16x2 + 8x + 1) = 6x(4x + 1)2. Side of square equals 4x + 1. Perimeter = 4(4x + 1) = 16x + 4. [3] appropriate methods, but with one computational error [2] found factors of polynomial, but did not find perimeter [1] correct answer, without work shown 54. (k + 7)2 55. (r + 3)2 56. (y – 8)2 57. 2(t + 3)2 9-8