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Math 1201 Factoring Review Name:______________________ Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Factor the binomial a. b. ____ 2. Factor the trinomial a. b. ____ 3. Factor the binomial a. b. ____ ____ ____ ____ ____ c. d. . c. d. . c. d. 4. Factor: a. b. c. d. 5. Factor: a. b. c. d. 6. Factor: a. b. c. d. 7. Which set of algebra tiles represents a. ? c. b. ____ . d. 8. Expand and simplify: a. b. c. d. 9. Factor: a. b. c. d. 1|Page ____ 10. Expand and simplify: a. b. c. d. ____ 11. Expand and simplify: a. b. c. d. ____ 12. Expand and simplify: a. b. c. d. ____ 13. Which polynomial, written in simplified form, represents the area of this rectangle? 8x – 4y x + 5y a. b. c. d. ____ 14. Expand and simplify: a. b. c. d. ____ 15. Each shape is a rectangle. Write a polynomial, in simplified form, to represent the area of the shaded region. 3x + 8 x +6 x –3 a. b. ____ 16. Factor: a. b. 2x + 6 c. d. c. d. ____ 17. Identify this polynomial as a perfect square trinomial, a difference of squares, or neither. a. Perfect square trinomial b. Difference of squares c. Neither 2|Page ____ 18. Factor: a. b. c. d. ____ 19. Factor: a. b. c. d. ____ 20. Determine the area of the shaded region in simplified form then factored form. (Both figures are squares) x–5 2x + 7 a. b. c. d. Short Answer 21. Write an expression for the width of this rectangle. 2a Area = 2a 2+ 12ab 22. Expand and simplify: 23. Expand and simplify: 24. Factor: 25. 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? 3|Page 26. Multiply this pair of binomials. Sketch and label a rectangle to illustrate the product. 27. Factor . 28. factor . 29. Write a polynomial to represent the area of this rectangle. Simplify the polynomial. 6x + 3y 4x – 5y 30. The volume of a right rectangular prism is represented by the trinomial Use factoring to determine the length and width of the prism when the height is . . (V=lwh) 4|Page Math 1201 Factoring Review Answer Section MULTIPLE CHOICE 1. ANS: C 2.ANS:B 3.ANS:A 4.ANS:C 5. ANS: D 6.ANS:D 7.ANS:B 8.ANS:B 10. ANS: D 11.ANS:C 12.ANS:A 13.ANS:D 14. ANS: D 15.ANS:A 16.ANS:D 17.ANS:B 18. ANS: A 19.ANS:B 20.ANS:B SHORT ANSWER 21. ANS: 22.ANS: 23.ANS: 24. ANS: 25. 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. 26. x x (x)(x) =x 2 9 (9)(x) = 9x –4 (–4)(x) = –4x (–4)(9) = –36 27. 28. 29. 30. When the height of the prism is , both the length and width are . 5|Page