Review for Exam #3 Math 0980
Topics 6.1 - 8.1
1. Write the expression using exponents:
a) 444444xxxxxxxyyy
b) 5
4•5
4•5
4•5
4aaab
Simplify each of the following:
2. x5•x2•x9
3. (- 4x2y5)3
4. (2xy)3 (4x3)
5. 3
3⎟
⎠
⎞
⎜
⎝
⎛
c
ab
6. (-3x)2
7. -2x2•x
8. 40 (x3y5)0
9. 3(xy2)0
10. 5(x0y3)2 (There are no problems 11 – 15)
16. (2x3 - 4x2 + 3x - 2) + (5x3 - 4x + 7)
17. (5x3 - 5x2 + 5) - (3x3 - x2 + 3x -2)
18. Identify each of the following as a monomial,
bimonial, or trinomial:
a) 2x2y - 3x
b) 5x3y2z4
c) 7x2 - 3x5 + 8
d) 7x5 - 12y4
19. Write in decending order:
6x + 32x3 - 4x4 + x2
20. What is the degree of the polymonial in # 19?
21. Evaluate: 3x2 - 4x + 7 when x = -2
22. 3x(3x2 - 5x + 5)
23. -2x3 (5x2 - 3x + 9)
24. (x - 3)(x + 5)
25. - 2x5 •8x2
26. (2x + 5)(3x - 2)
27. (x - 1)(x2 - 3x + 5)
28. (x - 3)2
29. (6x - 1)(6x + 1)
30. 3x(2x - 1)(5x + 4)
31. Add, then multiply: 4x2, -8x2, 2x3
32. (18x4 + 15x3 - 12x2) ÷ 3x3
33. (6x2 - 7x - 20) ÷ (2x + 3)
34. (3x - 2y)(5x + 2y)
35. Identify the base and the exponent in each of the
following:
a) 8x5 b) (-6x2)3 c) (8x)2
d) -5x3 e) 93
Factor by grouping:
36. 6a3 - 4a2b - 9ab2 + 6b3
37. x2 + 2x + 4y + 2xy
Factor out the greatest common factor.
38. 40m9 + 12m6 - 16 m4
39. 11m2 - 24r3
40. 3x5 - 6x4 + 12x3
41. 18x5y - 6xy
Find the greatest common factor of the terms.
42. 64a10b4, 40a6b10
43. 24x5y3, 12xy2, 36x2
Decide if the expression is completely factored.
44. (3x + 5y)(3x - 5y)
45. 7(m - 2) + n(m - 2)
46. (2x)(5y) + 11xy
Factor as completely as possible.
47. x2 - x - 30 48. x2 - 5x - 14
49. 4x3 + 8x2y - 32xy2
50. x2 + 9x + 18 51. x2 + 10x + 16
52. 3x2 - 18xy + 24y2
53. x2 + 6x + 2 54. 8x2 + 14xt + 3t2
55. 9z2 + 6z - 8 56. 10x2 + 23x + 12
57. 6x2 - 26x - 20 58. 10x2y2 + 3xy2 - 4y2
59. x2 + 12xy + 36y2
60. 49x2 - 9 61. x2 - 25
62. 8x2 - 32 63. x4 - 81
Solve by factoring:
64. x2- x - 12 = 0
65. 2x2 + 7x = - 3
66. 2(2x - 2) = -15x2
(There are no problems 67 – 71)
Find the value for which each of the following rational
expressions is undefined:
72.
()()
13
4
+− xx
73.
(
)
6
18
2
−
−
−
x
x
x
74. 4
5
2
−
+
x
x
