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. |