14.5E: Exercises
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Recognize and Use the Appropriate Method to Factor a Polynomial Completely
In the following exercises, factor completely.
1. 2n2+13n−7
(2n−1)(n+7)
2. 8x2−9x−3
3. a5+9a3
a3(a2+9)
4. 75m3+12m
5. 121r2−s2
(11r−s)(11r+s)
6. 49b2−36a2
7. 8m2−32
8(m−2)(m+2)
8. 36q2−100
9. 25w2−60w+36
(5w−6)2
10. 49b2−112b+64
11. m2+14mn+49n2
(m+7n)2
12. 64x2+16xy+y2
13. 7b2+7b−42
7(b+3)(b−2)
14. 30n2+30n+72
15. 3x4y−81xy
3xy(x−3)(x2+3x+9)
16. 4x5y−32x2y
17. k4−16
(k−2)(k+2)(k2+4)
18. m4−81
19. 5x5y2−80xy2
5xy2(x2+4)(x+2)(x−2)
20. 48x5y2−243xy2
21. 15pq−15p+12q−12
3(5p+4)(q−1)
22. 12ab−6a+10b−5
23. 4x2+40x+84
4(x+3)(x+7)
24. 5q2−15q−90
25. 4u5v+4u2v3
u2(u+1)(u2−u+1)
26. 5m4n+320mn4
27. 4c2+20cd+81d2
prime
28. 25x2+35xy+49y2
29. 10m4−6250
10(m−5)(m+5)(m2+25)
30. 3v4−768
31. 36x2y+15xy−6y
3y(3x+2)(4x−1)
32. 60x2y−75xy+30y
33. 8x3−27y3
(2x−3y)(4x2+6xy+9y2)
34. 64x3+125y3
35. y6−1
(y+1)(y−1)(y2−y+1)
36. y6+1
37. 9x2−6xy+y2−49
(3x−y+7)(3x−y−7)
38. 16x2−24xy+9y2−64
39. (3x+1)2−6(3x−1)+9
(3x−2)2
40. (4x−5)2−7(4x−5)+12
41. Explain what it mean to factor a polynomial completely.
Answers will vary.
42. The difference of squares y4−625 can be factored as (y2−25)(y2+25). But it is not completely factored. What more must be done to completely factor.
43. Of all the factoring methods covered in this chapter (GCF, grouping, undo FOIL, ‘ac’ method, special products) which is the easiest for you? Which is the hardest? Explain your answers.
Answers will vary.
44. Create three factoring problems that would be good test questions to measure your knowledge of factoring. Show the solutions.
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?