CHAPTER 8 Polynomials

# 8.7 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 |

## Evaluate a Polynomial for a Given Value of the Variable

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. |

## Multiply Monomials

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. 3 | 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. |

## Multiply a Trinomial by a Binomial

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. |

## Multiply Conjugates Using the Product of Conjugates Pattern

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

57. | 58. |

59. | 60. |

61. | 62. |

## Recognize and Use the Appropriate Special Product Pattern

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. |

# 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. |

# 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. |

# Practice Test Answers

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

4. | 5. | 6. |

7. | 8. | 9. |

10. | 11. | 12. |

13. | 14. | 15. |

16. 424 feet |