Question: Help me understand Given f(x) = x 4 + 5x 3 - x 2 - 17x + 12 a. Divide f(x) by (x + 4)

Help me understand

Given f(x) = x4 + 5x3 - x2 - 17x + 12

a. Divide f(x) by (x + 4) and determine if it is a factor. Explain why or why not.

If it is a factor, determine the resulting zero.

b. Divide f(x) by (x - 3) and determine if it is a factor. Explain why or why not.

If it is a factor, determine the resulting zero.

c. Use the remainder theorem to check if 2x + 1 is a factor. Explain the results. If it is a factor, determine the resulting zero.

d. Use the remainder theorem to find f(1). Explain the results. If it is a zero, determine the resulting factor.

e. How many possible zeros are there?

f.List the possible zeros as determined by the Rational Root Theorem.

g. Use the information above to find ALL the (actual) zeros of the function.

h. Write f(x) as a product of its factors, taking into consideration the multiplicity of the zeros.

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