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.)
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
(b) Write the polynomial as a product of linear factors.
(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.)
3.Consider the following.
P(x) = (1 − 3x)/(1 − x)
Check for intercepts. (If an answer does not exist, enter DNE.)
(x, y) =
(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
6. Consider the following function.
f(x) = x4 + 25×2 + 144
Find all the zeros of the function. (Enter your answers as a
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