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Math 0980 Exam Review: Topics 6.1 - 8.1 - Prof. Linda A. Franko, Exams of Algebra

A review for exam #3 of math 0980, covering topics 6.1 to 8.1. It includes problems on simplifying expressions, identifying monomials, factoring, and solving equations. Students are encouraged to check their answers and use the review as a guide for studying.

Typology: Exams

Pre 2010

Uploaded on 08/10/2009

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Review for Exam #3 Math 0980
Topics 6.1 - 8.1
1. Write the expression using exponents:
a) 444444xxxxxxxyyy
b) 5
45
45
45
4aaab
Simplify each of the following:
2. x5x2x9
3. (- 4x2y5)3
4. (2xy)3 (4x3)
5. 3
3
c
ab
6. (-3x)2
7. -2x2x
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
pf3

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Review for Exam #3 Math 0980

Topics 6.1 - 8.

  1. Write the expression using exponents:

a) 444444xxxxxxxyyy

b)

aaab

Simplify each of the following:

  1. x

5

  • x

2

  • x

9

  1. (- 4x

2 y

5 )

3

  1. (2xy)

3 (4x

3 )

c

ab

  1. (-3x)

2

  1. -2x

2

  • x

0 (x

3 y

5 )

0

  1. 3(xy

2 )

0

  1. 5(x

0 y

3 )

2

( There are no problems 11 – 15)

  1. (2x

3

  • 4x

2

  • 3x - 2) + (5x

3

  • 4x + 7)
  1. (5x

3

  • 5x

2

      • (3x

3

  • x

2

  • 3x -2)
  1. Identify each of the following as a monomial,

bimonial, or trinomial:

a) 2x

2 y - 3x

b) 5x

3 y

2 z

4

c) 7x

2

  • 3x

5

  • 8

d) 7x

5

  • 12y

4

  1. Write in decending order:

6x + 32x

3

  • 4x

4

  • x

2

  1. What is the degree of the polymonial in # 19?
  2. Evaluate: 3x

2

  • 4x + 7 when x = -
  1. 3x(3x

2

  • 5x + 5)
  1. -2x

3 (5x

2

  • 3x + 9)
  1. (x - 3)(x + 5)
    • 2x

5

  • 8x

2

  1. (2x + 5)(3x - 2)
  2. (x - 1)(x

2

  • 3x + 5)
  1. (x - 3)

2

  1. (6x - 1)(6x + 1)
  2. 3x(2x - 1)(5x + 4)
  3. Add, then multiply: 4x

2 , -8x

2 , 2x

3

  1. (18x

4

  • 15x

3

  • 12x

2 ) ÷ 3x

3

  1. (6x

2

  • 7x - 20) ÷ (2x + 3)
  1. (3x - 2y)(5x + 2y)
  2. Identify the base and the exponent in each of the

following:

a) 8x

5 b) (-6x

2 )

3 c) (8x)

2

d) -5x

3 e) 9

3

Factor by grouping:

  1. 6a
  • 4a

b - 9ab

  • 6b
  1. x
  • 2x + 4y + 2xy

Factor out the greatest common factor.

  1. 40m
  • 12m
  • 16 m
  1. 11m
  • 24r
  1. 3x
  • 6x
  • 12x
  1. 18x

y - 6xy

Find the greatest common factor of the terms.

  1. 64a

b

, 40a

b

  1. 24x

y

, 12xy

, 36x

Decide if the expression is completely factored.

  1. (3x + 5y)(3x - 5y)
  2. 7(m - 2) + n(m - 2)
  3. (2x)(5y) + 11xy

Factor as completely as possible.

  1. x
  • x - 30 48. x
  • 5x - 14
  1. 4x
  • 8x

y - 32xy

  1. x
  • 9x + 18 51. x
  • 10x + 16
  1. 3x
  • 18xy + 24y
  1. x
  • 6x + 2 54. 8x
  • 14xt + 3t
  1. 9z
  • 6z - 8 56. 10x
  • 23x + 12
  1. 6x
  • 26x - 20 58. 10x

y

  • 3xy
  • 4y
  1. x
  • 12xy + 36y
  1. 49x
  • 9 61. x
  1. 8x
  • 32 63. x

Solve by factoring:

  1. x

2

  • x - 12 = 0
  1. 2x

2

  • 7x = - 3
  1. 2(2x - 2) = -15x

2

(There are no problems 67 – 71)

Find the value for which each of the following rational

expressions is undefined:

xx +

2 − −

x x

x

2 −

x

x

  1. Give an example of an expression that would not

be defined if x = 5 or x = -

Reduce to lowest terms:

2 5 3

5 2 3

x y z

x y z

ab

ab 3

2 4

2

2

x

x x

x

x

Add/Subtract/Multiply or Divide as indicated. Reduce

your answers to lowest term.

y

x

y

x

x +

x

2

x +

  1. Simplify:

2

2

4

r

p

r

p

Remember to take this exam as though it were the

actual exam. Take an hour when you will not be

disturbed, don’t use any notes or other aids. Now

check your answers. Use this as a guide to help you

decide where your time is best spent when studying.