# 1.consider the following function. f(x) = 3×4 + 9×2 + 6 (a) find

1.Consider the following function.

f(x) = 3×4 + 9×2 + 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 − 8×3 + 17×2 − 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.

(5×3 + 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 + 25×2 + 144

Find all the zeros of the function. (Enter your answers as a

comma-separated list.)

x =