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
3
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.