1.Consider the following function. f(x) = 3x4 + 9x2 + 6 (a) Find the zeros algebraically. (Enter your answers as a comma-separated list....

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. (If an answer does not exist, enter DNE.) (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 =