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1 Name: lass: ate: I: Polynomials Test RETKE Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. 5x 8 2x 7 2. (y 2 ) 8 What is the simplified form of each expression? a. 7x 15 b. 7x 56 c. 10x 56 d. 10x 15 a. y 256 b. y 10 c. 2y 16 d. y (2xy 4 ) 2 (xy) 8 4 a. x 6 b. 4y 2 x 6 c. 4x 10 y 16 d. 2x 6 y ( 4g 4 h 4 ) 2 (g 2 h 3 ) 7 a. 16g 15 h 16 b. 16g 22 h 29 c. g 22 h d. 16g 22 h m 6 m 2 a. m 4 b. m 12 c. m 2 5p 3 ˆ 2 1 m 4 d. m 8 a. 5m 4 p 6 b. 25m 4 5p c. 25p 6 m 4 d. 10m 4 2p 6 7. biologist studied the populations of white-sided jackrabbits and black-tailed jackrabbits over a 5-year period. The biologist modeled the populations, in thousands, with the following polynomials where x is time, in years. White-sided jackrabbits: 7.2x 2 7.5x lack-tailed jackrabbits: 6.4x 2 5.9x What polynomial models the total number of white-sided and black-tailed jackrabbits? a. 13.6x x c. 13.6x x b. 13.6x x 5.7 d. 13.6x x 5.7 1

2 Name: I: Simplify. ssume that no denominator is equal to zero. 8. 2a 3 ˆ 3 b 24b 5 a. a 6 3b 2 b. a 9 3b 2 c. a 9 12b 2 d. a 9 b m 5 n 6 2mn 3 p 3 a. 14n 9 p 3 m 6 b. 14m 6 n 9 p 3 c. 14n 9 m 6 p 3 d. 14n 3 p 3 m 4 Find the degree of the polynomial a 3 b a 4 b 6 6a 7 b 4 a. 10 b. 11 c. 14 d. 12 rrange the terms of the polynomial so that the powers of x are in descending order xy 2 + x 2 y 5 2x 3 + y 2 a. 2x 3 + x 2 y 5 + 5xy 2 + y 2 c. y 2 + 5xy 2 + x 2 y 5 2x 3 b. 2x 3 + y 2 + x 2 y 5 + 5xy 2 d. 2x 3 + x 2 y 5 + 5xy 2 + y 2 Find the sum or difference p 4q 2 ˆ q q2 6p + 8p 2 ˆ a. 8p 2 5q 2 + 4p q c. 8p 2 5q p q b. 8p 2 3q p q d. 8p 2 5q p q Solve the equation (n 11) = (2n 3) a. -11 b. 11 c. 33 d x 2 3x = (7x 2 + 5x) (2x ) a. -2 b. 2 c. 8 d. -8 Find the product. 15. ( r 7) ( r + 2) a. r 2 5r 14 b. r 2 14 c. r 2 + 9r 14 d. r 5 2

3 Name: I: 16. ( 5k + 5) 5k 2 ˆ + 3k 7 a. 25k 3 40k 2 20k 35 c. 5k 2 2k 2 b. 5k 2 15k 35 d. 25k 3 40k k g 5hˆ a. 49g 2 70gh 25h 2 c. 49g 2 25gh + 25h 2 b. 49g h 2 d. 49g 2 70gh + 25h ( 3c + 8) ( 3c 8) a. 9c b. 6c c. 9c c 64 d. 9c Find the area of the rectangle. a. 15a 7 b 13 b. 50a 7 b 13 c. 15a12b 42 d. 50a 12 b Simplify: 7x 2 (2x 3) 4x(x 2 5x + 3) 2(x 1) a. 10x 3 x x 2 c. 18x 3 41x 2 10x + 2 b. 18x 3 41x x 2 d. 10x 3 x 2 14x Find the area of the shaded region. a. 13x 2 + 9x 6 b. 13x 2 + 9x + 6 c. 47x x + 6 d. 47x x Simplify (x + 2) 3 a. x b. x 2 + 4x + 4 c. 8x 3 + 4x 2 d. x 3 + 6x x + 8 3

4 Name: I: 23. Find the area of the triangle. a. 14x 12 b. 28x 12 c. 14x 28 d. 14x Find the perimeter a. 16x 4 y 2 b. 17x 4 y 2 c. 34x 4 y 2 d. 17x 8 y Solve. 7x 8 > 13x + 4 a. x < -2 b. x > -2 c. x < 2/3 d. x > 2/3 26. Which compound inequality has the solution set shown in the graph? a. 3 p < 3 b. 3 < p 3 c. 3 < p < 3 d. p 3 or p < Which of the following is an example of the associative property? a. b + (3 + c) = b + (c + 3) c. b(3 + c) = b(3) + b(c) b. b + (3 + c) = (b + 3) + c d. b + (3 + c) = (3 + c) + b 28. What is the slope-intercept form of the equation of a line with slope -2 and y-intercept 4? a. y = 2x 4 b. y = 4x 2 c. y = 4x + 2 d. y = 2x Find the slope-intercept form of the equation of the line that passes through (2, -3) and is parallel to 15x + 3y = 11 a. y = 5x 13 b. y = 5x + 7 c. y = 5x + 7 d. y = 5x 13 4

5 I: Polynomials Test RETKE Review nswer Section MULTIPLE HOIE 1. NS: PTS: 1 IF: L2 REF: 7-3 Multiplying Powers With the Same ase OJ: To multiply powers with the same base NT: N.1.d N.1.f N.3.a.3.c.3.h ST: M.N.2.1 M.N.2.2 TOP: 7-3 Problem 2 Multiplying Powers in lgebraic Expressions OK: OK 1 2. NS: PTS: 1 IF: L2 REF: 7-4 More Multiplication Properties of Exponents OJ: To raise a power to a power NT: N.1.d N.1.f N.3.a.3.c.3.h ST: M.N.2.2 TOP: 7-4 Problem 1 Simplifying a Power Raised to a Power OK: OK 1 3. NS: PTS: 1 IF: L3 REF: 7-4 More Multiplication Properties of Exponents OJ: To raise a product to a power NT: N.1.d N.1.f N.3.a.3.c.3.h ST: M.N.2.2 TOP: 7-4 Problem 4 Simplifying an Expression With Products OK: OK 1 4. NS: PTS: 1 IF: L4 REF: 7-4 More Multiplication Properties of Exponents OJ: To raise a product to a power NT: N.1.d N.1.f N.3.a.3.c.3.h ST: M.N.2.2 TOP: 7-4 Problem 4 Simplifying an Expression With Products OK: OK 1 5. NS: PTS: 1 IF: L2 REF: 7-5 ivision Properties of Exponents OJ: To divide powers with the same base NT: N.1.d N.1.f N.3.a.3.c.3.h ST: M.N.2.1 M.N.2.2 TOP: 7-5 Problem 1 ividing lgebraic Expressions OK: OK 1 6. NS: PTS: 1 IF: L3 REF: 7-5 ivision Properties of Exponents OJ: To raise a quotient to a power NT: N.1.d N.1.f N.3.a.3.c.3.h ST: M.N.2.1 M.N.2.2 TOP: 7-5 Problem 4 Simplifying an Exponential Expression OK: OK 1 7. NS: PTS: 1 IF: L4 REF: 8-1 dding and Subtracting Polynomials OJ: To classify, add, and subtract polynomials NT:.3.c.3.e TOP: 8-1 Problem 4 dding Polynomials KEY: polynomial trinomial standard form of a polynomial OK: OK 2 8. NS: When a power has a power, multiply the exponents. To divide two powers that have the same base, subtract the exponents. When a power has a power, multiply exponents. orrect! on't forget that 2 has a power! When subtracting bottom exponent from top, if bottom is bigger it stays on the bottom. PTS: 1 IF: verage OJ: Simplify expressions involving the quotient of monomials. NT: N 2 N 8 N 9 N 10 N 6 ST: N 1.01 N 1.01a N 1.01b N 1.02 TOP: Simplify expressions involving the quotient of monomials KEY: Monomials Simplify Expressions Quotients 1

6 I: 9. NS: Invert negative powers. When dividing, subtract the bottom exponent from the top exponent with the same base. If the answer is negative, the result goes on the bottom. If positive, the result goes on top. orrect! Subtract bottom exponent from top. If the exponent is negative, answer goes on bottom. The variable p has a negative exponent. Subtract bottom exponent from top. PTS: 1 IF: verage OJ: Simplify expressions containing negative exponents. NT: N 2 N 8 N 9 N 10 N 6 ST: N 1.01 N 1.01a N 1.01b N 1.02 TOP: Simplify expressions containing negative exponents KEY: Simplify Expressions Negative Exponents 10. NS: dd the exponents of the variables for each monomial. The degree of the polynomial is the highest degree of any of its monomials. dd the exponents of all 3 monomials. orrect! dd exponents of each monomial, not each exponent in like variables. Only add the exponents of the variables. PTS: 1 IF: verage OJ: Find the degree of a polynomial. NT: N 1 N 8 N 9 N 10 N 6 ST: N 1.01a N 1.02 N 1.01 TOP: Find the degree of a polynomial KEY: Polynomials egree of Polynomial 11. NS: The monomial with the highest power of x comes first. Then the second highest, and so on. The powers of y make no difference. orrect! If the base is not in the monomial, remember it is considered to be the zero power. scending order. e careful with your signs. PTS: 1 IF: verage OJ: rrange the terms of a polynomial in ascending or descending order. NT: N 2 N 8 N 9 N 10 N 6 ST: N 1.01 N 1.02 TOP: rrange the terms of a polynomial in ascending or descending order KEY: Polynomials rrange Terms 2

7 I: 12. NS: Group like terms together. Subtract like terms, making sure you subtract negatives (add). The power stays the same. e careful with your signs. e careful with your signs. e careful with your signs. orrect! PTS: 1 IF: verage OJ: Subtract polynomials. NT: N 2 N 8 N 9 N 10 N 6 ST: N 1.01 N 1.01b N 1.02 TOP: Subtract polynomials KEY: Polynomials Subtract Polynomials 13. NS: PTS: 1 IF: asic OJ: Solve equations involving polynomials. NT: N 2 N 8 N 9 N 10 N 6 ST: N 1.01 N 1.01b N 1.02 TOP: Solve equations involving polynomials KEY: Polynomials Solve Equations 14. NS: Multiply both monomials in the parentheses by what is on the outside. orrect! on't multiply what is added after the parentheses. on't forget to square p! PTS: 1 IF: verage OJ: Solve equations involving polynomials. NT: N 2 N 8 N 9 N 10 N 6 ST: N 1.01 N 1.01b N 1.02 TOP: Solve equations involving polynomials KEY: Polynomials Solve Equations 15. NS: r 2 + 2r 7r 14 r 2 5r 14 orrect! Use the FOIL method. Watch your signs. Use the FOIL method. PTS: 1 IF: asic OJ: Multiply two binomials by using the FOIL method. NT: N 2 N 8 N 9 N 10 N 6 ST: N 1.01 N 1.01b N 1.02 TOP: Multiply two binomials by using the FOIL method KEY: Multiply inomials FOIL Method 3

8 I: 16. NS: 25k 3 15k k 25k k 35 25k 3 40k k 35 Watch your signs. Multiply each number in the binomial by each number in the polynomial, adding exponents. Then add numbers of like powers. Multiply each number in the binomial by each number in the polynomial, adding exponents. Then add numbers of like powers. orrect! PTS: 1 IF: verage OJ: Multiply two polynomials by using the istributive Property. NT: N 2 N 8 N 9 N 10 N 6 ST: N 1.01 N 1.01b N 1.02 TOP: Multiply two polynomials by using the istributive Property KEY: Multiply Polynomials istributive Property 17. NS: Find the product using the square of a difference pattern. 49g 2 2( 35)gh + 25h 2 49g 2 70gh + 25h 2 Watch your signs. (a b) squared = a squared -2ab + b squared. (a -b) squared = a squared -2ab + b squared. orrect! PTS: 1 IF: verage OJ: Find the squares of differences. NT: N 2 N 8 N 9 N 10 N 6 ST: N 1.01 N 1.01b N 1.02 TOP: Find the squares of differences KEY: Multiply inomials Squares of ifferences 18. NS: Find the product using the square of a sum and a difference. 9c 2 64 Watch your signs. on't add, multiply. (a + b)(a -b) = a squared b squared. orrect! PTS: 1 IF: verage OJ: Find the squares of a sum and a difference. NT: N 2 N 8 N 9 N 10 N 6 ST: N 1.01 N 1.01b N 1.02 TOP: Find the squares of a sum and a difference KEY: Multiply inomials Squares of Sum and ifference 19. NS: PTS: NS: PTS: NS: PTS: 1 4

9 I: 22. NS: PTS: NS: PTS: NS: PTS: NS: PTS: NS: PTS: NS: PTS: NS: PTS: NS: PTS: 1 5

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