Honors Algebra 2: Factoring Extra Practice

• Class: Honors Algebra 2
• Author: Peter Atlas
• Algebra and Trigonometry: Structure and Method, Brown

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Factor Completely:

1. $$40zw + 8x^{2}w - 35z - 7x^{2}$$
2. Solution $$\left(5z + x^{2}\right)\left(8w - 7\right)$$
3. $$a^{3} - a^{2}b + ab^{2} - b^{3}$$
4. Solution $$\left(a^{2} + b^{2}\right)\left(a - b\right)$$
5. $$a^{6} - b^{6}$$
6. Solution $$\left(a - b\right)\left(a^{2} + ab + b^{2}\right)\left(a + b\right)\left(a^{2} - ab + b^{2}\right)$$
7. $$x^{4} + 25$$
8. Solution Non-factorable
9. $$6x^{2} + 42x + 60$$
10. Solution $$6\left(x + 2\right)\left(x + 5\right)$$
11. $$4x^{2}- 24x + 36$$
12. Solution $$4\left(x - 3\right)^{2}$$
13. $$75x^{2} + 120x + 48$$
14. Solution $$3\left(5x + 4\right)^{2}$$
15. $$36 - 9x^{2}$$
16. Solution $$-9\left(x + 2\right)\left(x - 2\right)$$
17. $$2x^{2}y + xy - 2xz - z$$
18. Solution $$\left(2x + 1\right)\left(xy - z\right)$$
19. $$12x^{2}z + 8y^{2}z - 15x^{2}w - 10y^{2}w$$
20. Solution $$\left(3x^{2} + 2y^{2}\right)\left(4z - 5w\right)$$
21. $$y^{6} + 7y^{3} - 8$$
22. Solution $$\left(y + 2\right)\left(y^{2} - 2y + 4\right)\left(y - 1\right)\left(y^{2} + y + 1\right)$$
23. $$(x + y)^{3} - 27$$
24. Solution $$\left(x + y - 3\right)\left(x^{2} + 2xy + y^{2} +3x + 3y + 9\right)$$
25. $$x^{2} + 2x + 5$$
26. Solution Non-factorable
27. $$x^{16} - 1$$
28. Solution $$\left(x^{8} + 1\right)\left(x^{4} + 1\right)\left(x^{2} + 1\right)\left(x + 1\right)\left(x - 1\right)$$
29. $$5x^{2} - 42x - 27$$
30. Solution $$\left(5x + 3\right)\left(x - 9\right)$$
31. $$6a^{2} - 13a - 15$$
32. Solution $$\left(6a + 5\right)\left(a - 3\right)$$
33. $$15y^{2} + 17y - 18$$
34. Solution $$\left(5a + 9\right)\left(3y - 2\right)$$
35. $$14 p^{2} + 31p - 10$$
36. Solution $$\left(7p - 2\right)\left(2p + 5\right)$$
37. $$16t^{4} - 81$$
38. Solution $$\left(2t - 3\right)\left(2t + 3\right)\left(4t^{2} + 9\right)$$
39. $$81m^{8}- 1$$
40. Solution $$\left(3m^{2} - 1\right)\left(3m^{2} + 1\right)\left(9m^{4} + 1\right)$$
41. $$3z^{6} - 192$$
42. Solution $$3\left(z - 2\right)\left(z^{2} + 2z + 4\right)\left(z + 2\right)\left(z^{2} - 2z + 4\right)$$
43. $$6u^{6} - 8v^{3}$$
44. Solution $$2\left(3a^{6} - 4v^{3}\right)$$
45. $$16y^{4} - 72y^{2} + 81$$
46. Solution $$\left(2y - 3\right)^{2}\left(2y + 3\right)^{2}$$
47. $$(x - 1)^{2} - y^{2}$$
48. Solution $$\left(x - 1 + y\right)\left(x - 1 - y\right)$$
49. $$(r + s)^{2} - t^{2}$$
50. Solution $$\left(r + s + t\right)\left(r + s - t\right)$$
51. $$3ax - 6bx - 4a + 8b$$
52. Solution $$\left(3x - 4\right)\left(a - 2b\right)$$
53. $$(x + y)^{2} + 3(x + y) + 2$$
54. Solution $$\left(x + y + 1\right)\left(x + y + 2\right)$$
55. $$x^{4} - 3x^{2} - 40$$
56. Solution $$\left(x^{2} - 8\right)\left(x^{2} + 5\right)$$
57. $$x^{2a} - 3x^{a} + 2 \quad \forall a \in \mathbb{Z}$$
58. Solution $$\left(x^{a} - 1\right)\left(x^{a} - 2\right)$$
59. $$r^{2k} + 6r^{k} + 9 \quad \forall k \in \mathbb{Z}$$
60. Solution $$\left(r^{k} + 3\right)^{2}$$
61. $$h^{3} + 4h^{2} - 9h - 36$$
62. Solution $$\left(h + 3\right)\left(h - 3\right)\left(h + 4\right)$$
63. $$x^{2} - y^{2} + 4y - 4x$$
64. Solution $$\left(x + y - 4\right)\left(x - y\right)$$
65. $$x^{4} - (4x - 5)^{2}$$
66. Solution $$\left(x^{2} - 4x + 5\right)\left(x - 1\right)\left(x + 5\right)$$
67. $$(a + 5)^{2} + 12(a + 5) + 36$$
68. Solution $$\left(a + 11\right)^{2}$$
69. $$2a^{4} + 10a^{3} - 72a^{2}$$
70. Solution $$2a^{2}\left(a + 9\right)\left(a - 4\right)$$
71. $$9x^{2}y^{3} + 72x^{5}$$
72. Solution $$9x^{2}\left(y + 2x\right)\left(y^{2}- 2xy + 4x^{2}\right)$$

In the problem sets on §4.5 (p. 185) and §4.6 (p. 191) I only assigned even problems. Do the odd problems for extra practice. The answers are in the back of the book.