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# Factoring Polynomials Practice Problems

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Updated on Aug 24, 2011

To review these concepts, go to Factoring Polynomials Study Guide.

### Practice

Factor using the greatest common factor method.

1. 5x + 25
2. 100a + 300
3. 15a2b2 + 15ab2
4. 22xy + 11x
5. 5x + 9
6. 16x2 + 20x
7. x2y + 3x
8. 8x3 – 2x2 + 4x
9. –6x3 + 18x2y
10. 10x4y2 – 50x3y + 70
11. 6a2 – 39ab
12. 12a3b2c + 4a5bc2
13. 22x4y + 55x2y2
14. 8x2 + 12x + 20
15. 5f3 – 15f + 25
16. 30a3b2 + 20a2b + 35a4b2

Factor using the difference of two squares method.

1. 16r2 – 121
2. a2 – 9
3. x2y2 – 49
4. b2 – 100
5. r2s2
6. 36b2 – 100
7. a6b6
8. y2 – 64
9. 4x2 – 1
10. 25x2 – 4y2
11. x25 – 1
12. x4 – 16
13. b10 – 36
14. 16a2 – 25b2

Factor using the trinomial method.

1. x2 + 9x + 18
2. x2 + 6x + 8
3. x2 – 4x + 3
4. x2 + 7x + 12
5. x2 – 10x + 16
6. x2 – 15x + 14
7. x2 + 9x + 20
8. x2 – 12x + 20
9. x2 – 9x + 20
10. x2 – 11x + 30

Factor the trinomials.

1. a2a – 20
2. r2 – 7r – 18
3. x2 – 6x – 7
4. x2 + 3x – 10
5. x2 – 3x – 10
6. x2 – 7x – 8
7. x2 + 6x – 16
8. x2 – 4x – 21
9. x2 + x – 30
10. x2 – 3x – 18

### Solutions

1. 5(x + 5)
2. 100(a + 3)
3. 15ab(ab + b)
4. 11x(2y + 1)
5. prime—can't be factored
6. 4x(4x + 5)
7. x(xy + 3)
8. 2x(4x2x + 2)
9. – 6x2(x – 3y), or 6x2(– x + 3y)
10. 10(x4y2 – 5x3y + 7)
11. 3a(2a – 13b)
12. 4a3bc(3b + a2c)
13. 11x2y(2x2 + 5y)
14. 4(2x2 + 3x + 5)
15. 5(f 3 – 3f + 5)
16. 5a2b(6ab + 4 + 7a2b)
17. (4r + 11)(4r – 11)
18. (a + 3)(a – 3)
19. (xy + 7)(xy – 7)
20. (b + 10)(b – 10)
21. (r + s)(r &38211; s)
22. (6b + 10)(6b – 10)
23. (a3 + b3)(a3b3)
24. (y + 8)(y – 8)
25. (2x + 1)(2x – 1)
26. (5x + 2y)(5x – 2y)
27. prime—can't be factored (because x25 is not a perfect square)
28. (x2 + 4)(x2 – 4)
29. (b5 – 6)(b5 + 6)
30. (4a – 5b)(4a + 5b)
31. (x + 3)(x + 6)
32. (x + 4)(x + 2)
33. (x – 1)(x – 3)
34. (x + 4)(x + 3)
35. (x – 8)(x – 2)
36. (x – 14)(x – 1)
37. (x + 5)(x + 4)
38. (x – 10)(x – 2)
39. (x – 4)(x – 5)
40. (x – 6)(x – 5)
41. (a + 4)(a – 5)
42. (r – 9)(r + 2)
43. (x + 1)(x– 7)
44. (x + 5)(x – 2)
45. (x – 5)(x + 2)
46. (x – 8)(x + 1)
47. (x + 8)(x – 2)
48. (x – 7)(x + 3)
49. (x + 6)(x – 5)
50. (x – 6)(x + 3)

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