3 What is the degree of the polynomial function that generates the data shown below?

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1 hapter 04 Test Name: ate: 1 For the polynomial function, describe the end behavior of its graph. The leading term is down. The leading term is and down.. Since n is 1 and a is positive, the end behavior is up and. Since n is even and a is positive, the end behavior is down The leading term is. Since n is odd and a is positive, the end behavior is up and up. The leading term is. Since n is odd and a is positive, the end behavior is down and up. 2 For the polynomial function, describe the end behavior of its graph. The leading term is. Since n is odd and a is negative, the end behavior is down and up. The leading term is. Since n is even and a is negative, the end behavior is up and down. The leading term is. Since n is odd and a is negative, the end behavior is down and down. The leading term is. Since n is even and a is positive, the end behavior is up and up. 3 What is the degree of the polynomial function that generates the data shown below? opyright by Pearson Education Page 1 of 11

2 hapter 04 Test 4 Find all the solutions of the equation by factoring. 5 Find all the solutions of the equation by factoring. x 3 5x 2 = x(x + 4)(x 1); 0, 4, 1 x(x 3)(x 1); 0, 3, 1 x(x 4)(x 1); 0, 4, 1 x(x + 3)(x 1); 0, 3, 1 6 Use the Remainder Theorem and synthetic division to find for P(x) = 2x 4 7x 3 + x 2 10x You have several boxes with the same dimensions. They have a combined volume of 4x 4 21x 3 46x x ould represent the number of boxes you have? Yes; divides evenly. You get. No; does not divide evenly. You get with a remainder of. No; divides evenly. You get. opyright by Pearson Education Page 2 of 11

3 hapter 04 Test 8 Is a factor of? yes no 9 Write the polynomial in standard form. Then classify it by degree and by number of terms. p 3 2p + 2p 3 2p 6 2p; degree 6 binomial 2p 3 2p; cubic binomial 3p 3 2p; cubic binomial 3p 6 2p; degree 6 binomial 10 Write the polynomial in standard form. Then classify it by degree and by number of terms. 3 5x 9 5x 9 + 3; degree 9 binomial 5x 9 3; degree 9 binomial 5x 9 + 3; cubic binomial 5x 9 3; cubic binomial 11 Write the polynomial in standard form. Then classify it by degree and by number of terms. ; cubic trinomial ; quadratic trinomial ; quadratic trinomial ; cubic trinomial opyright by Pearson Education Page 3 of 11

4 hapter 04 Test 12 cylinder has a radius and a height of. Use 3.14 as and choose the graph that represents the volume V of the cylinder as a function of x. opyright by Pearson Education Page 4 of 11

5 hapter 04 Test 13 What is the difference? 14 What is the product? 15 Which polynomial has at least three zeros that are negative one which has multiplicity 2? 16 Write a polynomial function in standard form for the given set of roots. 3, 2, 0, 2 f(x) = 3x 4 2x 3 + 2x f(x) = x 4 + 3x 3 4x 2 12x f(x) = x 4 3x 3 2x f(x) = x 4 2x 3 + 2x 2 3x opyright by Pearson Education Page 5 of 11

6 hapter 04 Test 17 Write a polynomial function in standard form for the given set of roots. 2, i f(x) = f(x) = f(x) = f(x) = 18 Write a polynomial function in standard form for the given set of roots. 3, 0, 0, 1 f(x) = 3x 4 + x 2 f(x) = 3x f(x) = x 4 + 2x 3 3x 2 f(x) = x 4 3x 3 + x 2 19 Find the quotient and remainder. (x 3 + 3x 2 2x 4) (x 2) x 2 + x + 6, R 8 2x + 6, R 4 x 2 5x 8, R 2 x 2 + 5x + 8, R Find the quotient and remainder., R 14, R 14 opyright by Pearson Education Page 6 of 11

7 hapter 04 Test 21 For the equation, state the number of complex roots, the possible number of real roots, and the possible rational roots. x 3 6x x 6 = 0 3 complex roots; number of real roots: 3 or 1; possible rational roots: ±1, ±2, ±3, ±6 3 complex roots; number of real roots: 3 or 1; possible rational roots: ±2, ±3 2 complex roots; number of real roots: 3 or 1; possible rational roots: ±1, ±2, ±3, ±6 22 For the equation, state the number of complex roots, the possible number of real roots, and the possible rational roots. 10x 4 13x 3 21x x + 8 = 0 0 complex roots; number of real roots: 4, 2 or 0; possible rational roots: ±1, ±2, ±4 0, 2, or 4 complex roots; number of real roots: 4, 2 or 0; possible rational roots: ±1, ±2, ±4, ±8 4 complex roots; number of real roots: 4, 2 or 0; possible rational roots: ±1, ±2, ±4, ±8, 23 Factor the expression. Then find all the roots. x 3 2x 2 5x = 0 x(x 3)(x 2); 0, 3, 2 x(x 2.5) 2 ; 0, 2.5 x(x 2 7x 5); 0, x(x 2 2x 5); 0, 24 Factor the expression. Then find all the roots. ; 0, 4, 2 ; 0, ; 0, ; 0, -4, -2 opyright by Pearson Education Page 7 of 11

8 hapter 04 Test 25 One x-intercept of the graph of the cubic function x 3 3x 2 x + 3 is. What are the other zeros? 3, 1, Use synthetic division and the Remainder Theorem to find P(a). P(x) = 4 x x 5 ; a = Use synthetic division and the Remainder Theorem to find P(a). P(x) = x 3 8x 2 + 5x 7; a= Expand the binomial. opyright by Pearson Education Page 8 of 11

9 hapter 04 Test 29 Expand the binomial. 30 Expand the binomial. 31 You take measurements of the distance traveled by an object that is increasing its speed at a constant rate. The distance traveled d as a function of time t can be modeled by a quadratic function. What is the quadratic function that models distances of 21 ft at 1 s, 59 ft at 2 s, and 141 ft at 4 s? opyright by Pearson Education Page 9 of 11

hapter 04 Test 32 Using the given data for the average salary of the top 5% earners in the United States, explain why a linear model would more likely represent salary growth over time than a

10 hapter 04 Test 32 Using the given data for the average salary of the top 5% earners in the United States, explain why a linear model would more likely represent salary growth over time than a quadratic model would. linear model would continually rise whereas a quadratic model would have down-and-down end behavior. quadratic model implies a turning point. Since we know that the average salary of the United States fluctuates continually, the best model is quadratic. linear model is unrealistic because salaries fluctuate continually over time. Salaries tend to decrease over long periods of time. quadratic model implies a turning point with a minimum as the vertex of a parabola. Since we know that the average salary of the United States has a definite minimum value, the best model is quadratic. linear model would continually rise whereas a quadratic model would have down-and-down end behavior. quadratic model seems to imply a turning point, and then a decline; eventually going to 0. Since we know that the average salary will not go to zero, the best model is linear. linear model would increase, then decrease. It would take the shape of an absolute-value function. quadratic model would have the shape of a parabola with a maximum. Since we know that the average salary of the United States will peak at some point and decrease linearly, the best model is linear. opyright by Pearson Education Page 10 of 11

11 hapter 04 Test 33 ompare function to b(x) graphed below. Which function has a greater stretch factor? How many times greater is it? a(x), as great b(x), 3x as great b(x), as great a(x), 3x as great 34 How many roots does the following equation have? Find all of the roots of the equation. 1, 2, i 2, 2 2, 2, i, i 1, 2, i opyright by Pearson Education Page 11 of 11

Advanced Math Quiz Review Name: Dec Use Synthetic Division to divide the first polynomial by the second polynomial.

Advanced Math Quiz Review Name: Dec Use Synthetic Division to divide the first polynomial by the second polynomial. Advanced Math Quiz 3.1-3.2 Review Name: Dec. 2014 Use Synthetic Division to divide the first polynomial by the second polynomial. 1. 5x 3 + 6x 2 8 x + 1, x 5 1. Quotient: 2. x 5 10x 3 + 5 x 1, x + 4 2.