Factoring – Distribution, GCF, and Grouping
Name: __________________________
Simplify each product. Write in standard form. All work should be shown on another sheet of paper.
1. 4(a – 3)
2. –5(x – 2)
3. –3x2 (x2 + 3x)
4. 4x3 (x – 3)
5. –5x2 (x2 + 2x + 1)
6. 3x(x2 – 5x – 3)
7. – x2 (–2x 2 + 3x – 2)
8. 4d2(d2 – 3d – 7)
9. 5m3(m + 6)
10. a2(2a + 4)
11. 4(x2 – 3) + x(x + 1)
12. 4x(5x – 6)
13. (x + 5)(x + 4)
14. (3w + 4)(2w – 1)
15. (x + 3)(2x – 5)
16. (3s – 4)(s – 5)
17. (5x – 3)(4x + 2)
18. (5x – 2)(x + 3)
19. (b + 8)(2b – 5)
20. (3x + 5)(5x – 7)
21. (x – 9)(3x + 5)
22. (x + 2)(2x2 – 3x + 2)
23. (2n – 3)(n2 – 2n + 5)
24. (2x2 – 9x + 11)(2x + 1)
Determine the GCF from the following expressions. All work should be shown on another sheet of paper.
25. 8x – 4
26. 14d – 2
27. 15x + 45x2
28. x2 + 3x
29. 6h2 – 8h
30. 12n3 – 8n
31. 9 – 27x3
32. x3 – 5x2
33. 21x3 + 56x4
34. 3z4 – 15z3 – 9z2
35. 3y3 – 8y2 – 9y
36. 16m5 – 8m4 + 12m2
37. 6y4 + 9y3 – 27y2
38. 8d4 + 4d2 + 12d
39. 18c4 – 9c2 + 7c
Factor the following by finding the GCF. All work should be shown on another sheet of paper.
40. 8x – 4
41. 14d – 2
42. 15x + 45x2
43. x2 + 3x
44. 6h2 – 8h
45. 12n3 – 8n
46. 9 – 27x3
47. x3 – 5x2
48. 21x3 + 56x4
49. 3z4 – 15z3 – 9z2
50. 3y3 – 8y2 – 9y
51. 16m5 – 8m4 + 12m2
52. 6y4 + 9y3 – 27y2
53. 8d4 + 4d2 + 12d
54. 18c4 – 9c2 + 7c
Factor the following by grouping. All work should be shown on another sheet of paper.
55. 2x3 + 8x2 + x + 4
56. 8x 4 + 6x - 28x 3 −21
57. 5x 3− x2 + 15x - 3
58. x3+ 3x 2 - 4x - 12
59. 10x 3 − 25x2 + 4x −10
60. 4x3 - 20x 2 - 3x + 15
61. A rectangular field has a width that is five less than 4 times the length. Write an expression in terms of length to
represent the area of the field. Simplify your answer and write in standard form.
62. One side of a square has length 2x – 3. Write an expression to represent the area of the square. Simplify your
answer and write in standard form.
63. A circular pond will be placed on a square piece of land. The length of a side of the square is 2x. The radius of the
pond is x. The part of the square not covered by the pond will be planted with flowers. What is the area of the region
that will be planted with flowers? Write your answer in factored form. (Area of a Circle = πr2)
64. A square poster of length 3x is to have a square painting centered on it. The length of the painting is 2x. The area
of the poster not covered by the painting will be painted black. What is the area of the poster that will be painted
black? Write your answer in factored form.
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Factoring – Quadratics
Name: ________________________________
Factor each expression. All work should be shown on another sheet of paper. (a ≠ 1)
1. 2x 2 + 3x + 1
2. 2n 2 + n - 6
3. 4m 2 – 1
4. 7n2 + 9n + 2
5. 2y 2 - 9y - 5
6. 3x 2 - 10x + 8
7. 5x 2 + 2x - 3
8. 16c2 – 49
9. 5x 2 - 22 x + 8
10. 9x 2 – 4
11. 7y 2 + 19y + 10
12. 2y 2 + 9y + 7
13. 2x 2 + 5x - 3
14. 4a2 – 81
15. 15x 2 - 19x + 6
16. 8x 2 - 30x + 25
17. 8x 2 + 65x + 8
18. 10x 2 + 3x – 4
19. 22 x 2 + 51x - 10
20. 4y 2 - 11y - 3
21. 256a2 – 1
22. 5x 2 - 11x + 2
23. 9r2 – 256
24. 3x 2 - x - 4
Factor each expression. All work should be shown on another sheet of paper. (a = 1)
25. x2 + 8 x + 16
26. d 2 + 8d + 7
27. y2+ 6y + 8
28. b2 - 2b - 3
29. x 2 + 12 x + 32
30. n2 + n - 6
31. x2 – 9
32. y2 + 16y - 17
33. n2 + 16n - 36
34. x2 - 14x + 48
35. x2 + 3x – 40
36. x2 – 121
37. n2 - 23n + 60
38. b2 + 3b - 4
39. x2 - 8x + 15
40. c2 - 3c - 10
41. y2 + 6y - 55
42. p2 - 12p – 28
43. b2 + 9b + 14
44. x2 – 169
45. r2 - 14r - 51
Factor each expression. All work should be shown on another sheet of paper.
46. 3x 2 + 8x + 4
47. x 2 - 5 x + 6
48. 5x 2 - 2x - 7
49. 7x 2 - 10x + 3
50. 5x 2 - 33 x - 14
51. x2 + 14x + 45
52. 5y 2 - 3y - 2
53. x2 - 6x - 27
54. m2 - 4m - 21
55. 3x 2 + 17x + 10
56. 3x 2 - 7x - 6
57. 6x 2 - 11x + 4
58. x2 - 5x - 24
59. b2 - 4b - 60
60. 24y 2 + 41y +12
61. 10y 2 - 29y + 10
62. n2 - 15n + 26
63. 6y 2 - 5y + 1
64. 3y2 - 16y - 12
65. b2 + 4b – 12
66. n2- 2n - 63
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