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

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

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).

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. i41

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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.