Factoring Review - Answers

Factoring Review - Answers

Part I – GCF

1. 2z2 + 16 = 2(z2 + 8) / 6. 6c4 – 9c = 3c(2c3 – 3 )
2. 8g2 + 20g = 4g(2g + 5) / 7. -9a6 –27a5 –12a3 =-3a3(3a3 + 9a2 +4)
3. 8r3 – 36r – 4 = 4(2r3 – 9r – 1) / 8. 18c2 + 4c = 2c(9c + 2)
4. 28s2 + 20s = 4s(7s + 5) / 9. –8y6 + 4y4 + 8 = 4(-2y6 + y4 + 2)
5. 16x3 + 4x2 + 36x = 4x(4x2 + x + 9) / 10. 35v6 –15v3 –15v2 =5v2(7v4 – 3v –3)

Part II – Difference of Two Squares

11. x2 – 16 = (x + 4)(x – 4) / 16. x4 – 1 = (x2 + 1) (x2 – 1)
12. 36u6 – 81w2 = (6u3 + 9w)(6u3 - 9w) / 17. 100k4 – 49 = (10k2 + 7) (10k2 – 7)
13. h2 + 36 = PRIME / 18. p8 – 25 = (p4 + 5) (p4 – 5)
14. 64 – 25j10 = (8 + 5j5)(8 – 5j5) / 19. 4 – 36v12 = (2 + 6v6)(2 – 6v6)
15. 9s2 – 16t2 = (3s + 4t)(3s - 4t) / 20. 144 + y4 = PRIME

Part III – Trinomial Squares

21. x2 + 8x + 16 = (x + 4)2 / 26. x2 – 4xy + 4y2 = (x – 2y)2
22. x2 – 14x + 49 = (x – 7)2 / 27. 2x2 – 40x + 200 = 2(x – 10)2
23. 9x2 + 18xy + 9y2 = 9(x + y)2 / 28. 12x2 + 36xy + 27y2 = 3(2x + 3y)2
24. 16x2 – 56xy + 49y2 = (4x – 7y)2 / 29. a4 + 14a2 + 49 = (a2 + 7)2
25. x2 –6x + 9 = (x – y)2 / 30. 4x4 + 4x2 + 1 = (2x2 + 1)2

Part IV – Trinomials in the form x2 + bx + c

31. x2 – 6x – 7 = (x + 1)(x – 7) / 36. x2 + 5x + 6 = (x + 2)(x + 3)
32. s2 + 12s + 35 = (s + 7)(s + 5) / 37. w2 – 6w – 5 = PRIME
33. p2 – 9p + 20 = (p – 4)(p – 5) / 38. k2 + 3k – 4 = (k – 1)(k + 4)
34. b2 + 5b – 36 = (b – 4)(b + 9) / 39. h2 – 9h – 36 = (n + 3)(n – 12)
35. p2 – 8p – 9 = (p + 1)(p – 9) / 40. w2 + 2w – 15 = (w – 3)(w + 5)

Part V – Trinomials in the form ax2 + bx + c

41. 10x3 + 45x2 – 25x=2a(a – 8)(a – 11) / 46. 2a3 – 38a2 +176a=5x(2x – 1)(x + 5)
42. 16m2 –48m +11=(4m – 1)(4m – 11) / 47. 2q5 –12q4 –80q3=2q3(q + 4)(q – 10)
43. 3x2 – 5x – 2 = (3x + 1)(x – 2) / 48. 3d5 +18d4 +15d3= 3d3(d + 5)(q + 1)
44. 20c2 – 63c + 49 = (5c – 7)(4c – 7) / 49. 2x2 – x –15 = (2x + 5)(x – 3)
45. 4u2 + 37u + 63 = (4u + 9)(u + 7) / 50. 3a2 – 4a + 1 = (3a – 1)(a – 1)

Part VI – Grouping

51. 4x5 + 6x3 +6x2 +9=(2x2 + 3)(2x2 + 3) / 56. 7y2 –14y + by – 2b = (y – 2)(7y +b)
52. c6– c4 –c2+ 1=(c2 +1)(c + 1)2(c – 1)2 / 57. 2xy+3yz-4x+3yz–z=(3y – 1)(4x + z)
53. 4y5 +6y4+6y3+9y2= (2y4+3y4)(2y+3) / 58. 20a +12 –25ax –15x = (5a+3)(4-5x)
54. x13 + x7 + 2x6 + 2 = (x7+2)(x6 +1) / 59.4mna+4mnb+5na+5nb=(4mn+5n)(a+b)
55. 20g3 – 4g2 – 25g +5=(5g–1)(4g2–5) / 60. t2 – 9t + 3t – 27 = (t – 9)(t + 3)

Part VII – Mixed Factoring

61. d2 + d – 132 = (d – 11)(d + 12) / 66. 3n2 – 43n + 84 = (n –12)(3n – 7)
62. p2 – 100 = (p + 10)(p – 10) / 67. f2 + 121 = PRIME
63. 3v4 + 9v3 – 12v2 = 3v2(v – 1)(v + 4) / 68. 4x4 + 4x2 + 1 = (2x2 + 1) 2
64. 3h2 + 44h + 121 =(3n + 11)(n + 11) / 69.18c3–21c2–30c+35=(3c2 – 5)(6c – 7)
65. 9x10 + 12x5 + 4 = (3x5 + 2)2 / 70. z2 – 6z – 72 = (z + 6)(z – 12)