# 6.8 Chapter Review

# Review Exercises

## Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

1.
a) |
2.
a) |

## Determine the Degree of Polynomials

**In the following exercises, determine the degree of each polynomial.**

3.
a) b) c) d) e) 100 |
4.
a) b) c) d) e) |

## Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

5. | 6. |

7. | 8. |

9. | 10. |

11. | 12. |

## Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

13. | 14. |

15. | 16. |

17. Find the sum of | 18. Subtract |

In the following exercises, evaluate each polynomial for the given value.

19. Evaluate when: a) b) c) |
20. Evaluate when: a) b) c) |

21. A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial . Find the revenue received when dollars. |
22. Randee drops a stone off the 200 foot high cliff into the ocean. The polynomial gives the height of a stone seconds after it is dropped from the cliff. Find the height after seconds. |

In the following exercises, multiply the monomials.

23. | 24. |

25. | 26. |

## Multiply a Polynomial by a Monomial

In the following exercises, multiply.

27. | 28. |

29. | 30. |

31. | 32. |

33. | 34. |

35. | 36. |

## Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using: a) the Distributive Property, b) the FOIL method, c) the Vertical Method.

37. | 38. |

In the following exercises, multiply the binomials. Use any method.

39. | 40. |

41. | 42. |

43. | 44. |

45. | 46. |

In the following exercises, multiply using a) the Distributive Property, b) the Vertical Method.

47. | 48. |

In the following exercises, multiply. Use either method.

49. | 50. |

## Square a Binomial Using the Binomial Squares Pattern

In the following exercises, square each binomial using the Binomial Squares Pattern.

51. | 52. |

53. | 54. |

55. | 56. |

In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern.

57. | 58. |

59. | 60. |

61. | 62. |

In the following exercises, find each product.

63. | 64. |

65. | 66. |

67. | 68. |

## Divide a Polynomial by a Monomial

In the following exercises, divide each polynomial by the monomial.

69. | 70. |

71. | 72. |

73. | 74. |

75. | 76. |

## Greatest Common Factor of two or more expressions

In the following exercises, find the greatest common factor.

77. | 78. |

79. | 80. |

81. | 82. |

## Factor the Greatest Common Factor from a polynomial

In the following exercises, factor the greatest common factor from each polynomial.

83. | 84. |

85. | 86. |

87. | 88. |

89. | 90. |

## Factor by Grouping

In the following exercises, factor by grouping.

91. | 92. |

93. | 94. |

## Factor Trinomials of the Form

In the following exercises, factor each trinomial.

95. | 96. |

97. | 98. |

99. | 100. |

## Factor Trinomials of the Form

In the following exercises, factor each trinomial.

101. | 102. |

103. | 104. |

105. | 106. |

## Divide a Polynomial by a Monomial

In the following exercises, divide each polynomial by the monomial.

107. | 108. |

109. | 110. |

111. | 112. |

113. | 114. |

## Factor Binomials of the Form

In the following exercises, factorize using the difference of squares.

115. | 116. |

117. | 118. |

119. | 120. |

# Review Exercise Answers

1. a) binomial b) monomial c) trinomial d) trinomial e) other polynomial | 3. a) 3 b) 4 c) 2 d) 4 e) 0 | 5. |

7. | 9. | 11. |

13. | 15. | 17. |

19. a) b) 10 c) 22 | 21. 12,000 | 23. |

25. | 27. | 29. |

31. | 33. | 35. |

37.
a) b) c) |
39. | 41. |

43. | 45. | 47.
a) b) |

49. | 51. | 53. |

55. | 57. | 59. |

61. | 63. | 65. |

67. | 69. | 71. |

73. | 75. | 77. |

79. | 81. | 83. |

85. | 87. | 89. |

91. | 93. | 95. |

97. Prime or not factorable. | 99. | 101. |

103. | 105. | 107. |

109. | 111. | 113. |

115. | 117. | 119. |

# Chapter Practice Test

In the following exercises, simplify each expression. 1. |
2. For the polynomial a) Is it a monomial, binomial, or trinomial? b) What is its degree? |

3. | 4. |

5. | 6. |

7. | 8. |

9. | 10. |

11. | 12. |

13. | 14. |

15. | 16. A helicopter flying at an altitude of 1000 feet drops a rescue package. The polynomial gives the height of the package seconds after it was dropped. Find the height when seconds. |

17. Divide: | 18. Divide: |

19. Multiply: | 20. Factor: |

21. Factor: | 22. Factor: |

23. Factor: | 24. Factor: |

1. | 2. a) Trinomial, b) 4 | 3. |

4. | 5. | 6. |

7. | 8. | 9. |

10. | 11. | 12. |

13. | 14. | 15. |

16. 424 feet | 17. | 18. |

19. | 20. | 21. |

22. | 23. | 24. |