69 R.6 Factoring Polynomials 10. Which of the following is the correct factorization of x3 + 8? A. 1x + 223 B. 1x + 221x2 + 2x + 42 C. 1x + 221x2 - 2x + 42 D. 1x + 221x2 - 4x + 42 Factor out the greatest common factor from each polynomial. See Example 1. 11. 12m+ 60 12. 15r - 27 13. 8k3 + 24k 14. 9z4 + 81z 15. xy - 5xy2 16. 5h2j + hj 17. -4p3q4 - 2p2q5 18. -3z5w2 - 18z3w4 19. 4k2m3 + 8k4m3 - 12k2m4 20. 28r4s2 + 7r3s - 35r4s3 21. 21a + b2 + 4m1a + b 22. 6x1a + b2 - 4y1a + b2 23. 15r - 621r + 32 - 12r - 121r + 32 24. 14z - 5213z - 22 - 13z - 9213z - 22 25. 21m- 12 - 31m- 122 + 21m- 123 26. 51a + 323 - 21a + 32 + 1a + 322 27. Concept Check When directed to completely factor the polynomial 4x2y5 - 8xy3, a student wrote 2xy312xy2 - 42. When the teacher did not give him full credit, he complained because when his answer is multiplied out, the result is the original polynomial. Give the correct answer. 28. Concept Check Kurt factored 16a2 - 40a - 6a + 15 by grouping and obtained 18a - 3212a - 52. Callie factored the same polynomial and gave an answer of 13 - 8a215 - 2a2. Which answer is correct? Factor each polynomial by grouping. See Example 2. 29. 6st + 9t - 10s - 15 30. 10ab - 6b + 35a - 21 31. 2m4 + 6 - am4 - 3a 32. 4x6 + 36 - x6y - 9y 33. p2q2 - 10 - 2q2 + 5p2 34. 20z2 - 8x + 5pz2 - 2px Factor each trinomial, if possible. See Examples 3 and 4. 35. 6a2 - 11a + 4 36. 8h2 - 2h - 21 37. 3m2 + 14m+ 8 38. 9y2 - 18y + 8 39. 15p2 + 24p + 8 40. 9x2 + 4x - 2 41. 12a3 + 10a2 - 42a 42. 36x3 + 18x2 - 4x 43. 6k2 + 5kp - 6p2 44. 14m2 + 11mr - 15r2 45. 5a2 - 7ab - 6b2 46. 12s2 + 11st - 5t2 47. 12x2 - xy - y2 48. 30a2 + am- m2 49. 24a4 + 10a3b - 4a2b2 50. 18x5 + 15x4z - 75x3z2 51. 9m2 - 12m+ 4 52. 16p2 - 40p + 25 53. 32a2 + 48ab + 18b2 54. 20p2 - 100pq + 125q2 55. 4x2y2 + 28xy + 49 56. 9m2n2 + 12mn + 4 57. 1a - 3b22 - 61a - 3b2 + 9 58. 12p + q22 - 1012p + q2 + 25 Factor each polynomial. See Examples 5 and 6. 59. 9a2 - 16 60. 16q2 - 25 61. x4 - 16 62. y4 - 81 63. 25s4 - 9t2 64. 36z2 - 81y4 65. 1a + b22 - 16 66. 1p - 2q22 - 100 67. p4 - 625 68. m4 - 1296 69. x2 - 8x + 16 - y2 70. m2 + 10m+ 25 - n4 71. y2 - x2 + 12x - 36 72. 9m2 - n2 - 2n - 1 73. 8 - a3
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