Chapter 10 Final Exam Review
On a separate sheet of paper answer show your work and answers to the following
problems. Don’t forget to circle your answers
Identify the following polynomials by degree and number of terms:
3
2. 5x
3
5. − 2x + 3x − 5
1. 3x + 4x − 5
4
3
2
4. 4x + 2x
2
3. −9x + 2x + 3x − 2
6. 7x + 2
Multiply the following polynomials:
(
)
2
7. 2x 3x + 4x − 5
8 ( 2x + 4) (3x − 8)
10. (3x − 4) ( 2x − 5)
11.
13. (3x − 4) (3x − 4)
14. (3x + 4) (3x + 4)
(
16. x + 3
) ( x + 3)
9. (3x + 4) ( 2x − 5)
(3x − 4) (2x + 5)
(
2
12. (3x − 4) (3x + 4)
(
2
15. (3x − 5) 3x − 2x + 4
17. ( x + 2 ) x − 3x + 4
(
)
2
18. ( x +1) 2x − 5x + 9
Add or subtract the following polynomials:
(
2
19. ( 2x − 8) + 5x − 9
21.
(3x
2
)
20. (3x − 5) − ( 5x − 2 )
) (
+ 2x − 5 − 5x 2 − 3x − 2
)
(
3
) (
2
22. 3x − 2x + 6x + 2x
3
) − (−5x
3
+ 9x
)
23. What common mistakes do you need to be careful of when adding or subtracting polynomials?
Factor the following polynomials:
2
2
24. x + x − 30
2
27. 8x −18x − 45
30.
3y 2 −15y + 18
€
3
40. 8x +10x
3
2
29 2x + 10x + 8
2
32. 3b + 6b − 9
2
34. 2x + 8x − 24
€
2
2
2
31. 5m −10m − 40
2
36. x − 3x
26. 6x + 29x + 28
28. 15x −13x − 20
33. 4n + 12n + 8
€
2
25. x − 4x − 21
€
43. 4x + 8x − 9x −18
€
2
37. 4y − 9
3
41. x + 27x
3
€
2
2
€
44. 3x + 5x −12x − 20
2
2
35 3y −15y + 12
2
2
38. 3x +15
3
39. 4x − 36
2
42. 3x + 6x − 5x −10
2
45. ( x − 4) − 9
)
)
46. Describe how to factor a polynomial expression. Include how you know when and what types of
factoring to use as well as how you know the polynomial can’t be factored anymore.
Solving:
47. In what ways are solving polynomial equations similar to factoring polynomials? In what ways is
solving polynomial equations different than factoring polynomial expressions?
48. What do you do if you need to solve an equation with a quadratic polynomial, but you can’t factor it?
Solve these polynomial equations
2
2
50. x − 4x − 21 = 0
2
53. 3k −18k − 21 = 0
2
56. x − 36 = 13
2
59. 5x −180x = 0
49. x + x − 30 = 0
52. b + 5b = 0
55. x −10x = 0
58. x − 60 = −11
2
51. 3y −15y +18 = 0
2
2
2
57. 2m −14m = −3m
3
3
62. 4x + 24x + 36x = 0
2
65. 6x +10x + 9x +15 = 0
64. 3x +14x = 49
2
67. ( x − 2 ) + 3 = 19
2
60. x + 7x − 8x − 56 = 0
2
61. 2x − 4x − 30 = 0
2
54. x −121 = 0
3
2
63. 2x = 6x −1
2
3
2
66. ( x − 2 ) = 25
2
2
2
68. 3v + 36v + 49 = 8v
69. 5x = 125
Exciting “Completing the Square” section…Only the lucky get to do this.
Rewrite each quadratic from general from to vertex form by completing the square:
2
70. y = x + 4x +1
2
71. y = x + 6x + 2
2
72. y = 2x +16x − 7