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8.2E: Exercises

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Practice Makes Perfect

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

1. 10p3q,12pq2

Answer

2pq

2. 8a2b3,10ab2

3. 12m2n3,30m5n3

Answer

6m2n3

4. 28x2y4,42x4y4

5. 10a3,12a2,14a

Answer

2a

6. 20y3,28y2,40y

7. 35x3y2,10x4y,5x5y3

Answer

5x3y

8. 27p2q3,45p3q4,9p4q3

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

9. 6m+9

Answer

3(2m+3)

10. 14p+35

11. 9n63

Answer

9(n7)

12. 45b18

13. 3x2+6x9

Answer

3(x2+2x3)

14. 4y2+8y4

15. 8p2+4p+2

Answer

2(4p2+2p+1)

16. 10q2+14q+20

17. 8y3+16y2

Answer

8y2(y+2)

18. 12x310x

19. 5x315x2+20x

Answer

5x(x23x+4)

20. 8m240m+16

21. 24x312x2+15x

Answer

3x(8x24x+5)

22. 24y318y230y

23. 12xy2+18x2y230y3

Answer

6y2(2x+3x25y)

24. 21pq2+35p2q228q3

25. 20x3y4x2y2+12xy3

Answer

4xy(5x2xy+3y2)

26. 24a3b+6a2b218ab3

27. 2x4

Answer

2(x+4)

28. 3b+12

29. 2x3+18x28x

Answer

2x(x29x+4)

30. 5y3+35y215y

31. 4p3q12p2q2+16pq2

Answer

4pq(p2+3pq4q)

32. 6a3b12a2b2+18ab2

33. 5x(x+1)+3(x+1)

Answer

(x+1)(5x+3)

34. 2x(x1)+9(x1)

35. 3b(b2)13(b2)

Answer

(b2)(3b13)

36. 6m(m5)7(m5)

Factor by Grouping

In the following exercises, factor by grouping.

37. ab+5a+3b+15

Answer

(b+5)(a+3)

38. cd+6c+4d+24

39. 8y2+y+40y+5

Answer

(y+5)(8y+1)

40. 6y2+7y+24y+28

41. uv9u+2v18

Answer

(u+2)(v9)

42. pq10p+8q80

43. u2u+6u6

Answer

(u1)(u+6)

44. x2x+4x4

45. 9p215p+12p20

Answer

(3p5)(3p+4)

46. 16q2+20q28q35

47. mn6m4n+24

Answer

(n6)(m4)

48. r23rr+3

49. 2x214x5x+35

Answer

(x7)(2x5)

50. 4x236x3x+27

Mixed Practice

In the following exercises, factor.

51. 18xy227x2y

Answer

9xy(3x+2y)

52. 4x3y5x2y3+12xy4

53. 3x37x2+6x14

Answer

(x2+2)(3x7)

54. x3+x2x1

55. x2+xy+5x+5y

Answer

(x+y)(x+5)

56. 5x33x2+5x3

Writing Exercises

57. What does it mean to say a polynomial is in factored form?

Answer

Answers will vary.

58. How do you check result after factoring a polynomial?

59. The greatest common factor of 36 and 60 is 12. Explain what this means.

Answer

Answers will vary.

60. What is the GCF of y4, y5, and y10? Write a general rule that tells you how to find the GCF of ya, yb, and yc.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has 4 columns, 3 rows and a header row. The header row labels each column I can, confidently, with some help and no I don’t get it. The first column has the following statements: find the greatest common factor of 2 or more expressions, factor the greatest common factor from a polynomial, factor by grouping. The remaining columns are blank.

ⓑ If most of your checks were:

…confidently. Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific!

…with some help. This must be addressed quickly as topics you do not master become potholes in your road to success. Math is sequential - every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no - I don’t get it! This is critical and you must not ignore it. You need to get help immediately or you will quickly be overwhelmed. See your instructor as soon as possible to discuss your situation. Together you can come up with a plan to get you the help you need.


This page titled 8.2E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Chau D Tran.

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