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1 Name: _ lass: _ ate: Postssessment Polynomial Unit Multiple hoice Identify the choice that best completes the statement or answers the question. 1 Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 4 1x 2 2x + 5x 2 5x 2 2x + 4; quadratic trinomial 4x 2 2x +4; quadratic trinomial 6x 2 2x +4; quadratic trinomial 6x 2 8x +4; cubic trinomial 2 Write the polynomial in standard form. 4g g 3 + 3g g + 3g 2 g 3 3g 3 g 2 + 4g 2 g 3 3g 2 + 4g 2 g 3 + 3g 2 + 4g 2 3 etermine the degree of the polynomial: 4x 2 yz Match the expression with its name. 6x 3 9x + 3 cubic trinomial fourth-degree monomial quadratic binomial not a polynomial

2 5 Write the perimeter of the figure. 9x + 7x 11x + 3x x x 6 ssume f(x) = 3x 2x 3 +5 and g(x) = 2x 3 +5 x, find f(x)+g(x). 4x 3 + 4x x 3 2x x x 3 + 2x ssume f(w)=-w 2 4w 1 and g(w)=2w 2 + 5w - 2, find f(w) - g(w). -3w 2 + w 1 w 2 w 3 w 2 + w 3-3w 2-9w ssume f(x) = 3x 1 and g(x) = x 3 +2x+1, find f(x) g(x). 2x 3 +6x 2 +x+1 3x 4 x 3 +6x 2 +x 1 3x 4 +x 3 +6x 2 1 3x 4 +6x 2 +x 1 Page 2

3 9 Find the GF of the terms of the polynomial. 6x x 5 2x 2 2x 5 4x x 2 10 Use the GF of the terms to factor the polynomial. 8x 2 +24x 16 Ê 8 x 2 ˆ +3x 2 Ë Á 4x( 2x 4) 2(4x 2 +12x 8) 8x( x 2) Factor the following polynomials. 11 x 3 8 (x +2)(x 2 2x +4) (x 2)(x 2 2x +8) (x +2)(x 2 +2x +4) (x 2)(x 2 +2x +4) 12 12g g 2 18g 15 (2g 2 + 3)(6g 5) (2g 2 3)(6g + 5) (2g 2 5)(6g + 3) (2g 2 + 5)(6g 3) 13 3x 2 + 7x 6 (3x 2)(x 3) (x + 3)(3x + 2) (3x 2)(x + 3) (3x + 2)(x 3) Page 3

4 14 Use a graphing calculator to determine which type of model best fits the values in the table. x y linear model, it has a constant 1st difference cubic model, it has a constant 3rd difference quadratic model, it has a constant 2nd difference none of these 15 Find the zeros of y = x(x + 2)(x + 4). Then graph the equation. 2, 4, 2 0, 2, 4 2, 4 0, 2, 4 Page 4

5 16 Write a polynomial function in standard form with zeros at 3, 4, and 2. f(x) = x x 2 5x 2 f(x) = x 3 5x 2 2x + 24 f(x) = x 3 5x 2 2x 11 f(x) = x x 2 48x 11 Solve the polynomial. 17 x 2 9x + 23 = 0 x = 32 x = 81 x = 23 no solution 18 Evaluate the polynomial 2x 3y for x = 3 and y = For which values of m and n will the binomial m 3 n 2 + m 2 n 5 have a positive value? m = 2, n = 2 m = 1, n = 2 m = 3, n = 1 m = 3, n = 5 20 fireworks company has two types of rockets called Zinger 1 and Zinger 2. The polynomial 16t t gives the height in feet of Zinger 1 at t seconds after launch. The polynomial 16t t gives the height of Zinger 2 at t seconds after launch. If the rockets are launched at the same time and both explode 6 seconds after launch, how much higher is Zinger 2 than Zinger 1 when they explode? 414 ft 60 ft 90 ft 324 ft Page 5

6 21 Write a polynomial with zeros at 4, -2, and 1. Then graph the function. P(x) = (x+4)(x 2)(x+1) P(x) = (x 4)(x+2)(x 1) P(x) = (x 4)(x 2)(x 1) P(x) = (x+4)(x+2)(x+1) 22 etermine the number of real zeros possible for the polynomial, p(x) = x 5 +4x 3 2x or less five or less 1 or more five or more Page 6

7 23 Using the polynomial, f(x) = 2x 3 +4x 8, explain how the degree and leading coefficient will effect the end behavior. ecause the degree is odd, the ends will point in opposite directions, and because the leading coefficient is positive the graph will increase from right to left. ecause the degree is odd, the ends will point in opposite directions, and because the leading coefficient is positive the graph will decrease from right to left. ecause the degree is odd, the ends will point in the same direction, and because the leading coefficient is positive the graph will increase from right to left. ecause the degree is odd, the ends will point in the same direction, and because the leading coefficient is positive the graph will decrease from right to left. Page 7

8 24 escribe the transformation of the parent function, f(x) = x 3, to obtain the function g(x) = (x+4) Then make a graph of the new function. The new graph will be right 4 and up 1. The new graph will be left 4 and up 1. The new graph will be right 4 and down 1. The new graph will be left 4 and down 1. Page 8

9 25 Find the inverse of P(x) = (x 4) etermine if the inverse is a function. P 1 (x) = x +4 +4, yes it is a function. P 1 (x) = x +2 +4, no it is not a function. P 1 (x) = x +4 +4, yes it is a function. P 1 (x) = x +4 +4, no it is not a function. 26 etermine if the following is a function, then state the domain and range: y = 2x 3 +2x 2 4x +4. Yes, it is a function. omain: ÔÏ Ìy y R Yes, it is a function. omain: Ï Ô Ìy y 4 No, it is not a function. omain: ÔÏ Ìy y R No, it is not a function. omain: Ï Ô Ìy y 4 Page 9

10 27 The graph below is a model of the polynomial: y = x 4 5x Is the graph a function? What is the domain and range of the function? Yes, it is a function. omain: Ï Ô Ìy y R No, it is not a function. omain: ÔÏ Ìy y 4 Yes, it is a function. omain: Ï Ô Ìy y 2.25 No, it is not a function. omain: ÔÏ Ìy y 2.25 Page 10

11 28 The graph below is a model of the polynomial: y = x 4 5x Is the inverse of this graph a function? Why? Yes, it is a function. It passes the horizontal line test. No, it is not a function. It fails the horizontal line test. Yes, it is a function. It passes the vertical line test. No, it is not a function. It fails the vertical line test. 29 Ian designed a child s tent in the shape of a cube. The volume of the tent in cubic feet can be modeled by the equation s 3 64 = 0, where s is the side length. What is the side length of the tent? 4 feet 16 feet 64 feet 8 feet 30 Miguel is designing shipping boxes that are rectangular prisms. One shape of box with height h in feet, has a volume defined by the function V(h) = h(h 4)(h 10). Graph the function. What is the maximum volume for the domain 0 < h < 10? Round to the nearest cubic foot. 10 ft 3 32 ft 3 30 ft 3 25 ft 3 Page 11

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