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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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