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Name: _____________________________
Solving – ZPP, Factoring, Square Roots, and Quadratic Formula
Use the Zero-Product Property to solve each equation. Show all work on another sheet of paper.
1. (x + 5)(x - 3) = 0
2. (x - 2)(x + 9) = 0
3. (b - 12)(b + 12) = 0
4. (2n + 3)(n - 4) = 0
5. (x + 7)(4x - 5) = 0
6. (2x + 7)(2x - 7) = 0
7. (3x - 7)(2x + 1) = 0
8. (8y - 3)(4y + 1) = 0
9. (5x + 6)(4x + 5) = 0
Solve by factoring. Show all work on another sheet of paper.
10. x2 + 5x + 6 = 0
11. b2 - 7b - 18 = 0
12. r2 - 4 = 0
13. x2 + 8x - 20 = 0
14. y2 + 14y + 13 = 0
15. s2 - 3s - 10 = 0
16. x2 + 7x = 8
17. 3x2 – 12x = 0
18. h2 + 10h = -21
19. 2t2 + 8t - 64 = 0
20. 3a2 - 36a + 81 = 0
21. 5x2 - 45x = 0
22. 8y2 – 44y = 0
23. 3n2 - 11n + 10 = 0
24. 2x2 - 7x - 9 = 0
25. 2n2 - 5n = 12
26. 9m2 – 49 = 0
27. 5s2 - 17s = -6
28. 6m2 = 13m + 28
29. 4a2 = 8a
30. 4r2 = r + 3
Solve by finding square roots. Show all work on another sheet of paper.
31. x2 = 16
32. x2 - 144 = 0
33. 3x2- 27 = 0
34. x2 – 16 = 0
35. x2 = 25
36. x2 – 8 = 10
37. 3x2 = 300
38. 4x2 + 5 = 41
39. 4x2 + 6 = 7
40. 25x2 - 7 = 74
41. 3x2 - 75 = 0
42. 4x2 - 8 = 32
Solve each equation. Show all work on another sheet of paper.
43. (x - 9)(x + 8) = 0
44. x - 9x - 10 = 0
45. (c - 21)(c + 21) = 0
46. (x - 12)(5x - 13) = 0
47. x2 - 400 = 0
48. x2 + 6x - 91 = 0
49. a2 + 6a - 72 = 0
50. 4x2 + 8x - 21 = 0
51. 20d2 - 82d + 80 = 0
52. 3n2 + 12n - 288 = 0
53. 2s2 - 13s - 24 = 0
54. x2 + 5x = 150
55. 5x2 - 8 = 72
56. 30a2 + 121a - 21 = 0
57. c2 - 81 = 0
58. x2 + 306 = -35x
59. x2 = 121
60. x2 - 21x + 108 = 0
Use the quadratic formula to solve each equation. If an equation has no solutions, write no solution. If
necessary, round to the nearest hundredth. All work should be shown on another sheet of paper.
61. x2 + 8x + 5 = 0
62. d2 - 4d - 96 = 0
63. 4x2 + 7x + 9 = 0
64. x2 + 13x + 30 = 0
65. 6w2 - 23w + 7 = 0
66. 5y2 = 17y + 12
67. 5a2 - 9a + 5 = 0
68. x2 + 3x – 8 = 0
69. x2 + 5x - 90 = 0
70. 8x2 + 25x + 19 = 0
71. 4a2 + 8a = 221
72. 3x2 - 19x + 40 = 0
Page 3
Factoring and Solving Review
Name: _____________________________
Factor the following expressions completely.
1) 12x4 – 21x2 + 9x
2) 32x5 + 80x
3) 18x4 + 6x – 24
Solve the following equations.
4) 3x2 – 5x + 7 = 7
6) 35x2 – 10x = 0
5) 3x3 = 24x2
Factor the following expressions completely.
7) x2 + 10x – 24
8) 4x2 – 4x – 15
9) 3x2 – x – 14
Solve the following equations
10) 2x2 + x = 3
12) 6x2 = 5x + 4
11) x2 – 2x – 15 = 0
Factor the following expressions completely.
13) x2 – 121
14) 16x2 – 25
15) 9x2 – 169
Solve the following equations.
16) 2x2 – 98 = 0
18) 9x2 + 3 = 4
17) 2x2 + 3x = 4
Page 4
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