Math 1201 Unit 3 Factors and Products Final Review. Multiple Choice. 1. Factor the binomial. a. c. b. d. 2. Factor the binomial. a. c. b. d.
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1 Multiple Choice 1. Factor the binomial. 2. Factor the binomial. 3. Factor the trinomial. 4. Factor the trinomial. 5. Factor the trinomial. 6. Factor the trinomial. 7. Factor the binomial. 8. Simplify the expression, then factor. 9. Factor the trinomial. 10. Identify the greatest common factor of the terms in the trinomial. 11. Factor the trinomial. 12. Factor the trinomial. 13. Simplify the expression, then factor. June
2 14. Which expression represents the area of the shaded region? a. b. c. d. 15. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check. 16. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check. 17. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check. 18. Expand and simplify: 19. Expand and simplify: 20. Factor: 21. Factor: 22. Factor: 23. Factor: 24. Factor: 25. Factor: June
3 26. Which multiplication sentence does this set of algebra tiles represent? 27. Which set of algebra tiles represents? 28. Expand and simplify: 29. Expand and simplify: 30. Factor: 31. Expand and simplify: 32. Factor: 33. Expand and simplify: 34. Expand and simplify: June
4 35. Which polynomial, written in simplified form, represents the area of this rectangle? 8 x 4y x + 5y 36. Expand and simplify: 37. Expand and simplify: 38. Each shape is a rectangle. Write a polynomial, in simplified form, to represent the area of the shaded region. 39. Factor: 40. Factor: 41. Factor: 42. Identify this polynomial as a perfect square trinomial, a difference of squares, or neither. a. Perfect square trinomial c. Neither b. Difference of squares 43. Factor: June
5 44. Determine the area of the shaded region in factored form. Short Answer 45. Factor the binomial. 46. Factor the trinomial. 47. Write an expression for the width of this rectangle. 2a Area = 2a ab 48. Simplify, then factor. 49. Identify the greatest common factor of the terms in this set. 50. Expand and simplify: 51. Factor: 52. Find and correct the errors in this factorization. 53. Expand and simplify: 54. Factor: 55. Factor: 56. Find and correct the error(s) in this solution of factoring by decomposition. 57. Expand and simplify: 58. Factor: 59. Factor: 60. Factor fully: June
6 61. The area of a square is represented by the trinomial. Determine an expression for the perimeter of the square. Problem 62. a) Here are a student s solutions for factoring polynomials. Identify the errors in each solution. Write a correct solution. i) Factor: Solution: ii) Factor: Solution: b) What should the student have done to check her work? 63. A square is drawn inside a circle with radius. a) Write an expression for the area of the shaded region. b) Factor the expression. 64. This composite object is formed by a cone with a hemisphere on top. A formula for the volume of this object is: r h a) Factor this formula. b) Use both forms of the formula to calculate the volume of this composite object with radius 4 cm and height 10 cm. c) Which formula to do you prefer to use? Why? 65. Factor. Check by expanding. 66. Factor. Check by expanding. 67. Find the area of the rectangle. 5 b 6 3 b 2 June
7 Answers - MULTIPLE CHOICE 1. ANS: C 2. ANS: D 3. ANS: B 4. ANS: C 5. ANS: D 6. ANS: B 7. ANS: A 8. ANS: B 9. ANS: C 10. ANS: B 11. ANS: A 12. ANS: B 13. ANS: B 14. ANS: C 15. ANS: C 16. ANS: D 17. ANS: B 18. ANS: A 19. ANS: A 20. ANS: C 21. ANS: C 22. ANS: D 23. ANS: D 24. ANS: C 25. ANS: B 26. ANS: D 27. ANS: B 28. ANS: B 29. ANS: A 30. ANS: B 31. ANS: D 32. ANS: A 33. ANS: C 34. ANS: C 35. ANS: D 36. ANS: A 37. ANS: C 38. ANS: A 39. ANS: D 40. ANS: D 41. ANS: D 42. ANS: B 43. ANS: A 44. ANS: B SHORT ANSWER 45. ANS: 46. ANS: 47. ANS: 48. ANS: 49. ANS: 50. ANS: 51. ANS: 52. ANS: 53. ANS: 54. ANS: 55. ANS: 56. ANS: 57. ANS: 58. ANS: 59. ANS: 60. ANS: June
8 PROBLEM 61. ANS: 62. ANS: a) i) Correction: The student did not remove the common factor from the third term correctly. When the common factor is the same as the term, a factor of 1 remains. This must be written as a term in the factored polynomial. ii) Correction: When the student removed the common factor from the third term, she made a sign error. The sign should be negative, not positive. b) The student should have expanded her solutions to check that the trinomial was the same as the original trinomial each time. 63. ANS: a) The area of the shaded region is the area of the circle minus the area of the square. Use the formula for the area of a circle. To determine the area of the square, first determine the side length, s, of the square. Use the Pythagorean Theorem in right ABC. Use the formula for the area, A, of a square. The area, A, of the shaded region is:. b) 64. ANS: a) Factor each term of the binomial. June
9 b) c) Answers will vary. For example: I prefer to use the factored formula because it has only one fraction. 65. ANS: Two numbers with a sum of 1 and a product of are 7 and. So, Check that the factors are correct. Multiply the factors. This trinomial is the same as the original trinomial, so the factors are correct. 66. ANS: The greatest common factor is 8. Two numbers with a sum of and a product of 45 are. Check that the factors are correct. Multiply the factors. The trinomial is the same as the original trinomial, so the factors are correct. 67. ANS: Use the formula for the area, A, of a rectangle. Use the distributive property. The area of the rectangle is square units. June
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