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Factoring Special Cases

Factoring Special Cases. ALGEBRA 1 LESSON 9-7. pages 493–495  Exercises 1. ( c + 5) 2 2. ( x – 1) 2 3. ( h + 6) 2 4. ( m – 12) 2 5. ( k – 8) 2 6. ( t – 7) 2 7. (2 m + 5) 8. (7 d + 2) 9. (5 g – 4) 10. (5 g – 3) 2 11. (8 r – 9) 2. 12. (10 v – 11) 2

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Factoring Special Cases

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  1. Factoring Special Cases ALGEBRA 1 LESSON 9-7 pages 493–495  Exercises 1. (c + 5)2 2. (x – 1)2 3. (h + 6)2 4. (m – 12)2 5. (k – 8)2 6. (t – 7)2 7. (2m + 5) 8. (7d + 2) 9. (5g – 4) 10. (5g – 3)2 11. (8r – 9)2 12. (10v – 11)2 13. (x + 2)(x – 2) 14. (y + 9)(y – 9) 15. (k + 14)(k – 14) 16. (r + 12)(r – 12) 17. (h + 10)(h – 10) 18. (m + 15)(m – 15) 19. (w + 16)(w – 16) 20. (x + 20)(x – 20) 21. (y + 30)(y – 30) 22. (5q + 3)(5q – 3) 23. (7y + 2)(7y – 2) 24. (3c + 8)(3c – 8) 25. (2m + 9)(2m – 9) 26. (4k + 7)(4k – 7) 27. (12p + 1)(12p – 1) 28. (9v + 10)(9v – 10) 29. (20n + 11)(20n – 11) 30. (5w + 14)(5w – 14) 31. 3(m + 2)(m – 2) 32. 5(k + 7)(k – 7) 33. 3(x + 8)2 34. 2(t – 9)2 35. 6r(r + 5)(r – 5) 9-7

  2. Factoring Special Cases ALGEBRA 1 LESSON 9-7 44.a. Answers may vary. Sample: 4x2 + 24x + 36 b. because (2x)2 = 4x2, 2(2x • 6) = 24x, and 62 = 36 45. 25(2v + w)(2v – w) 46. 4(2p – 3q)2 47. 7(2c + 5d)2 48.m + m – 49.x + 50. 16(2g – 3h)2 51.p – 2 36. 7(h – 4)2 37. Answers may vary. Sample: Rewrite the first and last terms as a square. Check to see if the middle term is 2ab. Factor as a square binomial: 4x2 + 12x + 9 = (2x)2 + 12x + 32 = (2x)2 + 2(2x)(3) + 32 = (2x + 3)2; 9x2 – 30x + 25 = (3x)2 – 30x + 52 = (3x)2 – 2(3x)(5) + 52 = (3x – 5)2. 38. 4x2 – 121 is the difference of two squares. So the answer should be (2x + 11)(2x – 11). 39. 11, 9 40. 13, 7 41. 15, 5 42. 13, 9 43. 16, 14 1 2 1 3 1 2 1 3 1 2 2 2 1 2 9-7

  3. Factoring Special Cases ALGEBRA 1 LESSON 9-7 52.n + n – 53.k + 3 54.a. 3.14n2 – 3.14m2 = 3.14(n + m)(n – m) b. 285.74 in.2 55.a. 4(x + 5)(x – 5) b. 4(x + 5)(x – 5) c. The polynomial has a GCF that has two identical factors. d. 3(x + 5)(x – 5); no, because 3 does not have a pair of identical factors. 56. (8r3 – 9)2 57. (p3 + 20q)2 58. (6m2 + 7)2 59. (9p5 + 11)2 60. 3(6m3 – 7)(6m3 + 7) 61. (x10 – 2y5)2 62. 4(8g2 – 5h3)(8g2 + 5h3) 63. 5(3x2 – 2y)2 64. 37(g4 + h4)(g2 + h2)(g + h)(g – h) 65.a.t – 3; 4 b. (t + 1)(t – 7) 1 3 1 5 1 3 1 5 1 5 2 9-7

  4. Factoring Special Cases ALGEBRA 1 LESSON 9-7 75. (2t + 1)(2t + 7) 76. (5w + 1)(w – 9) 77. (3t + 8)(2t + 1) 78. (7m – 9)(3m + 1) 79. (7x – 9)(2x + 1) 80. (2y + 11)(2y + 5) 81. (3k – 2)(4k + 1) 82. 768; 3072; 12,288; 3 • 4n-1 83. 29; 37; 45; –11 + 8n 84. –11; –20; –29; 34 – 9n 85. 0.02; 0.002; 0.0002; 2000 • n 86. –32; 64; –128; (–2)n 66. a. (4 + 9n2)(2 + 3n)(2 – 3n) b. They are squares of square terms. c. Answers may vary. Sample: 16x4 – 1 67. 9 68. –12 69. 30 70. 5 71. 12 72. 2.5 73. (2d + 1)(d + 5) 74. (2x – 3)(x – 4) 1 10 9-7

  5. 87. 129.6; 777.6; 4665.6; 0.1(6)n–1 88. ; ; ; 10 • 89. 6 ; 8; 9 ; –1 + n 90. 8; 32; 128; • 4n–1 or • 4n–3 91.a.y = 11.4x + 64.8 b. 93 c. 79 87. 129.6; 777.6; 4665.6; 0.1(6)n–1 88. ; ; ; 10 • 89. 6 ; 8; 9 ; –1 + n 90. 8; 32; 128; • 4n–1 or • 4n–3 91.a.y = 11.4x + 64.8 b. 93 c. 79 87. 129.6; 777.6; 4665.6; 0.1(6)n–1 88. ; ; ; 10 • 89. 6 ; 8; 9 ; –1 + n 90. 8; 32; 128; • 4n–1 or • 4n–3 91.a.y = 11.4x + 64.8 b. 93 c. 79 32 125 32 125 32 125 64 625 64 625 64 625 128 3125 128 3125 128 3125 2 5 2 5 2 5 n–1 n–1 n–1 1 2 1 2 1 2 1 2 1 2 1 2 3 2 3 2 3 2 1 32 1 32 1 32 1 2 1 2 1 2 Factoring Special Cases ALGEBRA 1 LESSON 9-7 9-7

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