1.Consider the following function. f(x) = 3x4 + 9x2 + 6 (a) Find the zeros algebraically. (Enter your answers as a comma-separated list. If there are no real zeros, enter DNE.) x =

2.Consider the following function. f(x) = x4 - 8x3 + 17x2 - 8x + 16 (a) Find all zeros of the function. (Enter your answers as a comma-separated list.) x =

(b) Write the polynomial as a product of linear factors. f(x) =

(c) Use your factorization to determine the x-intercepts of the graph of the function. Use a graphing utility to verify that the real zeros are the only x-intercepts. (Enter your answers as a comma-separated list. If no x-intercepts exist, enter DNE.) x =

3.Consider the following. P(x) = (1 - 3x)/(1 - x) Check for intercepts. (If an answer does not exist, enter DNE.) x-intercept (x, y) =y-intercept (x, y) =

Check for vertical and horizontal asymptotes. (If an answer does not exist, enter DNE.) vertical asymptote x = horizontal asymptote y =

Check for holes. (x, y) =

4. Use synthetic division to divide. (5x3 + 7x + 2) ÷ (x + 2)

5. Find a polynomial function f(x) with real coefficients that has the given zeros. (There are many correct answers.) -1, -1, 5 + 3i f(x)=

6. Consider the following function. f(x) = x4 + 25x2 + 144 Find all the zeros of the function. (Enter your answers as a comma-separated list.) x =