Algebra II: Chapter 5 Review

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Name: Class: Date: ID: A Algebra II: Chapter 5 Review Simplify the expression. Give your answer in exponential form. 1. 7 3 8 6 6 ˆ a. 56 54 b. 7 9 8 12 c. 56 15 36 d. 7 18 8 Simplify the expression. 2. a b ˆ 6 a. a 7 b 7 c. a 6 b b. a 6 b 6 d. a 7 b 6 Complete the statement to describe the end behavior of the graph of the function. 3. f( x) = x 3 + 7x + 4 f(x) as x and f(x) as x +. 4. f( x) = 3x 3 x 2 + 4 f(x) as x and f(x) as x +. 5. f( x) = x 3 + x 2 7 f(x) as x and f(x) as x +. Find the sum or difference. 6. 5h 3 ˆ + 8h 9 6h 3 + 6h 4 ˆ a. h 3 + 2h 5 c. h 3 + 14h 13 b. h 3 + 2h 13 d. h 3 2h 5 7. 6q 5 + 8q 2 ˆ + 3 8q 5 3q 7 ˆ a. 2q 5 + 8q 2 3q + 10 c. 2q 5 + 8q 2 + 3q + 10 b. 14q 5 + 8q 2 3q 4 d. 14q 5 + 5q 2 4 8. ( 3x + 7) 5x 2 ˆ 6x + 2 1

Name: ID: A Find the product. 9. ( 3x + 2) 2x 2 ˆ 7x 4 10. ( 4x 1) 3x 2 ˆ 2x 4 11. Find the missing term: ( x + 3) 2 = x 2 + 6x +. a. 12 b. 3 c. 6 d. 9 12. A rectangle has a length of x 6 and a width of x 7. Which equation below describes the perimeter, P, of the rectangle in terms of x? a. P = 2x 13 c. P = x 2 13x + 42 b. P = 4x 26 d. P = x 13 Factor the polynomial completely. 13. 5x 3 + 5x 2 + 30x a. 5x(x + 1)(x + 6) c. 5x(x 2 + x + 6) b. 5 x 3 + x 2 ˆ + 6x d. x 5x 2 + 5x + 30 ˆ 14. n 5 + 216n 2 15. 4x 3 8x 2 + 3x 6 16. x 4 13x 2 + 36 Find the real-number solutions of the equation. 17. p 3 4p 2 = 0 a. 4, 5 c. 4, 4 b. 0, 4 d. 0, 4 Divide. 18. 11x 2 6x 3 ˆ + 10 + 3x ( 3x + 1) a. 2x 2 8 + 3x 2 + 3x + 1 b. 2x 2 7 3x + 3 + 3x + 1 c. 2x 2 8 3x + 2 + 3x + 1 d. 2x 2 7 + 3x 3 + 3x + 1 2

Name: ID: A 19. A rectangle has an area of x 3 2x 2 ˆ + 3x 18 square meters and a width of ( x 3) meters. Find its length, in terms of x. a. x 2 ˆ 2x + 3 meters c. x 2 + x + 6 ˆ meters b. x 2 ˆ + x + 3 meters d. x 2 2x + 6 ˆ meters Given polynomial function f and a zero of f, find the other zeros. 20. f( x) = x 3 + 12x 2 + 48x + 64; 4 List the possible rational zeros of the function using the rational zeros theorem. 21. f( x) = x 3 + 7x 9 a. ±1,±9 c. ±1,±3,±7,±9 b. ±1,±7,±9 d. ±1,±3,±9 22. g(x) = x 5 4x 3 + 2x + 12 a. ±1,±2,±3,±4,±6,±12 c. 4,1,2,12 b. 1,2,3,4,6,12 d. ±1,±2,±4,±12 Find all zeros of the polynomial function. 23. f(x) = 10x 4 + x 3 12x 2 x + 2 24. Use the graph to approximate the real zeros of the function. a. 2 b. 2, 3, 1, 1 c. 3, 1, 1 d. 1, 1, 3 25. The number C, in thousands, of videos rented each year from a local video store can be modeled by C = 0.096(t 3 + 3t 2 + 39t + 500), where t = 0 represents the year 1990. Using this function, what year would you expect 210.2 thousand movies to be rented? a. 2005 b. 2000 c. 1997 d. 1999 3

Name: ID: A Identify the number of solutions of the equation or the number of zeros of the function. 26. f( x) = 5x 3 9 Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. 27. 3, 0, 5 28. Describe the end behavior of the function f( x) = 3x 3 + 4x 4 2x 2 5. 29. Write the cubic function whose graph is shown. 30. Which cubic function s graph passes through the points 1,0 0,24 ˆ? a. f(x) = x 3 + 3x 2 + 38x + 24 c. f(x) = x 3 + 11x 2 + 34x + 24 b. f(x) = x 3 11x 2 34x 24 d. f(x) = x 3 3x 2 38x 24 4

ID: A Algebra II: Chapter 5 Review Answer Section 1. ANS: D PTS: 1 DIF: Level A REF: MAL20728 STA: MI.MIGLC.MTH.06.9-12.A2.5.3 TOP: Lesson 5.1 Use Properties of Exponents KEY: exponents simplify BLM: Knowledge 2. ANS: B PTS: 1 DIF: Level A REF: MAL20738 STA: MI.MIGLC.MTH.06.9-12.A2.5.3 TOP: Lesson 5.1 Use Properties of Exponents KEY: exponents simplify BLM: Knowledge 3. ANS: + ; PTS: 1 DIF: Level B REF: MAL20755 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 5.2 Evaluate and Graph Polynomial Functions KEY: polynomial end behavior graph function BLM: Analysis 4. ANS: ; + PTS: 1 DIF: Level B REF: MAL20756 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 5.2 Evaluate and Graph Polynomial Functions KEY: end behavior polynomial graph function BLM: Analysis 5. ANS: + ; PTS: 1 DIF: Level B REF: MAL20757 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 5.2 Evaluate and Graph Polynomial Functions KEY: polynomial end behavior graph function BLM: Analysis 6. ANS: A PTS: 1 DIF: Level B REF: MAL20772 STA: MI.MIGLC.MTH.06.9-12.A1.1.4 TOP: Lesson 5.3 Add, Subtract, and Multiply Polynomials KEY: polynomials subtract BLM: Knowledge 7. ANS: B PTS: 1 DIF: Level B REF: MAL20768 STA: MI.MIGLC.MTH.06.9-12.A1.1.4 TOP: Lesson 5.3 Add, Subtract, and Multiply Polynomials KEY: polynomials add BLM: Knowledge 8. ANS: 5x 2 + 9x + 5 PTS: 1 DIF: Level A REF: MAL20770 STA: MI.MIGLC.MTH.06.9-12.A1.1.4 TOP: Lesson 5.3 Add, Subtract, and Multiply Polynomials KEY: binomial subtract polynomials trinomial BLM: Knowledge 9. ANS: 6x 3 17x 2 26x 8 PTS: 1 DIF: Level A REF: MAL20773 STA: MI.MIGLC.MTH.06.9-12.A1.1.4 TOP: Lesson 5.3 Add, Subtract, and Multiply Polynomials KEY: binomial polynomial multiply trinomial BLM: Knowledge 1

ID: A 10. ANS: 12x 3 11x 2 14x + 4 PTS: 1 DIF: Level A REF: MAL20774 STA: MI.MIGLC.MTH.06.9-12.A1.1.4 TOP: Lesson 5.3 Add, Subtract, and Multiply Polynomials KEY: trinomial binomial polynomial multiply BLM: Knowledge 11. ANS: D PTS: 1 DIF: Level A REF: MAL20779 TOP: Lesson 5.3 Add, Subtract, and Multiply Polynomials KEY: multiply polynomials BLM: Comprehension 12. ANS: B PTS: 1 DIF: Level B REF: MAL20780 STA: MI.MIGLC.MTH.06.9-12.A1.1.4 TOP: Lesson 5.3 Add, Subtract, and Multiply Polynomials KEY: word polynomial add BLM: Application 13. ANS: C PTS: 1 DIF: Level A REF: MAL20783 STA: MI.MIGLC.MTH.06.9-12.A1.2.5 TOP: Lesson 5.4 Factor and Solve Polynomial Equations KEY: polynomial factor BLM: Knowledge 14. ANS: n 2 ( n + 6) n 2 ˆ 6n + 36 PTS: 1 DIF: Level B REF: 7f3de69e-cdbb-11db-b502-0011258082f7 TOP: Lesson 5.4 Factor and Solve Polynomial Equations KEY: Factoring difference of cubes sum of cubes BLM: Comprehension 15. ANS: ( x 2) 4x 2 ˆ + 3 PTS: 1 DIF: Level B REF: MAL20786 STA: MI.MIGLC.MTH.06.9-12.A1.2.5 TOP: Lesson 5.4 Factor and Solve Polynomial Equations KEY: polynomial factor BLM: Comprehension 16. ANS: ( x 2) ( x + 2) ( x 3) ( x + 3) PTS: 1 DIF: Level B REF: MAL20795 STA: MI.MIGLC.MTH.06.9-12.A1.2.5 TOP: Lesson 5.4 Factor and Solve Polynomial Equations KEY: polynomial factor BLM: Comprehension 17. ANS: D PTS: 1 DIF: Level A REF: MAL20797 STA: MI.MIGLC.MTH.06.9-12.A1.1.4 TOP: Lesson 5.4 Factor and Solve Polynomial Equations KEY: solve cubic factor zero product BLM: Comprehension 18. ANS: C PTS: 1 DIF: Level B REF: MAL20805 TOP: Lesson 5.5 Apply the Remainder and Factor Theorems KEY: polynomial divide BLM: Knowledge 19. ANS: C PTS: 1 DIF: Level B REF: MAL20814 STA: MI.MIGLC.MTH.06.9-12.A1.1.5 TOP: Lesson 5.5 Apply the Remainder and Factor Theorems KEY: word trinomial binomial polynomial divide BLM: Application 2

ID: A 20. ANS: There are no other zeros. PTS: 1 DIF: Level B REF: 7f3fbbf3-cdbb-11db-b502-0011258082f7 TOP: Lesson 5.5 Apply the Remainder and Factor Theorems KEY: Remainder theorem factor theorem zeros of a function BLM: Application 21. ANS: D PTS: 1 DIF: Level A REF: MAL20820 TOP: Lesson 5.6 Find Rational Zeros KEY: rational zeros theorem functions BLM: Knowledge 22. ANS: A PTS: 1 DIF: Level A REF: MAL20821 TOP: Lesson 5.6 Find Rational Zeros KEY: polynomial rational zeros BLM: Knowledge 23. ANS: 1, 1, 1 2, 2 5 PTS: 1 DIF: Level A REF: MAL20832 TOP: Lesson 5.7 Apply the Fundamental Theorem of Algebra KEY: polynomial zeros function roots BLM: Knowledge 24. ANS: D PTS: 1 DIF: Level A REF: MAL20842 TOP: Lesson 5.7 Apply the Fundamental Theorem of Algebra KEY: estimate root zero function cubic BLM: Knowledge 25. ANS: B PTS: 1 DIF: Level C REF: MAL20831 TOP: Lesson 5.7 Apply the Fundamental Theorem of Algebra KEY: solve equation word functions zeros BLM: Application 26. ANS: 3 PTS: 1 DIF: Level A REF: 7f40f508-cdbb-11db-b502-0011258082f7 TOP: Lesson 5.7 Apply the Fundamental Theorem of Algebra KEY: Fundamental theorem of algebra corollary of the fundamental theorem of algebra BLM: Knowledge 27. ANS: f( x) = x 3 2x 2 15x PTS: 1 DIF: Level A REF: MAL20840 NAT: NCTM 9-12.ALG.2.c TOP: Lesson 5.7 Apply the Fundamental Theorem of Algebra KEY: polynomial write function zeros leading coefficient BLM: Comprehension 28. ANS: f( x) as x and f( x) as x PTS: 1 DIF: Level B REF: MAL20853 TOP: Lesson 5.8 Analyze Graphs of Polynomial Functions BLM: Analysis KEY: graph end behavior 3

ID: A 29. ANS: f( x) = 1 2 ( x + 1) ( x 3) 2 PTS: 1 DIF: Level A REF: MAL20855 TOP: Lesson 5.9 Write Polynomial Functions and Models KEY: cubic function graph BLM: Knowledge 30. ANS: C PTS: 1 DIF: Level A REF: MAL20857 TOP: Lesson 5.9 Write Polynomial Functions and Models KEY: write function cubic x-intercept BLM: Analysis 4

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