1) Find all the zeros of f(x) = x4 - 2x3 - 31x2 + 32x + 240.

2) Identify and label the vertex and x-intercepts 2) Identify and label the vertex and x-intercepts. f(x) = 3x2 - 12x + 11 SKIP

3) Find all zeros and any relative maxima or minima. f(x) = x5 +x3 - 4x

4) Write the quadratic function in standard form: f(x) = -x2 – 4x + 1

5) Write the standard form of the equation of the parabola that has a vertex at (-4, -1) and passes through the point (-2, 4). SKIP

6) What is the remainder for (4x3 + 2x – 1) ÷ (x – 3)

7) List all the possible rational zero of f(x) = 12x3 + 21x2 + 4x – 9?

8) Find a polynomial function that has the given zeros: 1, - 5 , 5

9) Write the complex number in standard form: −8+ −24

10) Simplify –4i – (2 + 6i) and write the answer in standard form.

11) Simplify and write the answer in standard form.

12) Find all the real zeros of the polynomial f(x) = x4 – x3 – 20x2 and determine the multiplicity of each.

13) Describe the right and left hand behavior of the graph of q(x) = x4 – 4x2

14) Sketch a graph of the polynomial function that is a third-degree polynomial with three real zeros and a positive leading coefficient.

15) Use long division to divide: (x3 – 2x + 5) ÷ (x – 3)

16) Using the factor (x + 3), find the remaining factor(s) of f(x) =3x3 + 2x2 – 19x + 6 and write the polynomial in fully factored form.

17) Use Decartes’ Rule of Signs to determine the number of possible positive and negative real zeros of f(x) = -2x4 + 13x3 – 21x2 + 2x + 8

18) Find all the zeros, real and nonreal of the polynomial p(x)=x3 +11x

19) Find a polynomial of the lowest degree with real coefficients that has the zeros 0, -3, 2i and whose leading coefficient is one.

20) Joey correctly factored f(x) = x3 – 3x2 – 34x – 48 as f(x) = (x – 8)(x + 2)(x + 3).  Based on that result, Joey said that the graph of the polynomial will have zeros at  (–8, 0), (2, 0) and (3, 0).  Is he correct? A) Yes, Joey correctly identified the zeros of the polynomial. B) No, Joey should have set each binomial factor equal to zero and then solved for x to determine the zeros of the polynomial. C) No, Joey should only have positive values for the zeros of the polynomial. D) No, Joey should have written the zeros as (0, –8), (0, 2) and (0, 3).

21) Is x + 1 a factor of the polynomial function p(x) = x3 – 7x2 – 10x + 16? A) No, because p(–1) ≠ 0. B) No, because p(1) ≠ 0. C) Yes, because p(–1) = 0. D) Yes, because p(1) = 0.

22) Where does the graph of the function h(x) = x4 + 3x2 – 4 cross the x–axis? A) x = –2 and x = 2 B) x = –2, x = –1, and x = 2 C) x = –2, x = –1, and x = 1 D) x = –1 and x = 1

23) To model the path of a soccer ball, a student can use a quadratic equation such as  y = –x2 + 12x – 32, where y represents the height of the ball and x represents the horizontal distance that the ball traveled.  Part A:  Assume that the x–axis represents the ground.  How far did the soccer ball travel horizontally in the air? 

23) To model the path of a soccer ball, a student can use a quadratic equation such as  y = –x2 + 12x – 32, where y represents the height of the ball and x represents the horizontal distance that the ball traveled.  Part B:  The equation was modified to become y = (–x2 + 12x – 32)(x2 + 25).  What is/are the complex zero(s) of this new equation?