# Section 4A.4E: Exercises

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## Practice Makes Perfect

Recognize and Use the Appropriate Method to Factor a Polynomial Completely

In the following exercises, factor completely.

1. $$2n^2+13n−7$$

$$(2n−1)(n+7)$$

2. $$8x^2−9x−3$$

3. $$a^5+9a^3$$

$$a^3(a^2+9)$$

4. $$75m^3+12m$$

5. $$121r^2−s^2$$

$$(11r−s)(11r+s)$$

6. $$49b^2−36a^2$$

7. $$8m^2−32$$

$$8(m−2)(m+2)$$

8. $$36q^2−100$$

9. $$25w^2−60w+36$$

$$(5w−6)^2$$

10. $$49b^2−112b+64$$

11. $$m^2+14mn+49n^2$$

$$(m+7n)^2$$

12. $$64x^2+16xy+y^2$$

13. $$7b^2+7b−42$$

$$7(b+3)(b−2)$$

14. $$30n^2+30n+72$$

15. $$3x^4y−81xy$$

$$3xy(x−3)(x^2+3x+9)$$

16. $$4x^5y−32x^2y$$

17. $$k^4−16$$

$$(k−2)(k+2)(k^2+4)$$

18. $$m^4−81$$

19. $$5x5y^2−80xy^2$$

$$5xy^2(x^2+4)(x+2)(x−2)$$

20. $$48x^5y^2−243xy^2$$

21. $$15pq−15p+12q−12$$

$$3(5p+4)(q−1)$$

22. $$12ab−6a+10b−5$$

23. $$4x^2+40x+84$$

$$4(x+3)(x+7)$$

24. $$5q^2−15q−90$$

25. $$4u^5v+4u^2v^3$$

$$u^2(u+1)(u^2−u+1)$$

26. $$5m^4n+320mn^4$$

27. $$4c^2+20cd+81d^2$$

prime

28. $$25x^2+35xy+49y^2$$

29. $$10m^4−6250$$

$$10(m−5)(m+5)(m^2+25)$$

30. $$3v^4−768$$

31. $$36x^2y+15xy−6y$$

$$3y(3x+2)(4x−1)$$

32. $$60x^2y−75xy+30y$$

33. $$8x^3−27y^3$$

$$(2x−3y)(4x^2+6xy+9y^2)$$

34. $$64x^3+125y^3$$

35. $$y^6−1$$

$$(y+1)(y−1)(y^2−y+1)$$

36. $$y^6+1$$

37. $$9x^2−6xy+y^2−49$$

$$(3x−y+7)(3x−y−7)$$

38. $$16x^2−24xy+9y^2−64$$

39. $$(3x+1)^2−6(3x−1)+9$$

$$(3x−2)2$$

40. $$(4x−5)^2−7(4x−5)+12$$

## Writing Exercises

41. Explain what it mean to factor a polynomial completely.

42. The difference of squares $$y^4−625$$ can be factored as $$(y^2−25)(y^2+25)$$. 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.