Factor a function given a zero

Question

Given that 4−4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable.

f(x)=x⁴−7x³+12x²+128x−384

Answer 1

Since 4-4i is a root, so is 4+4i.

The product of (x-4+4i) and (x-4-4i) is x² - 8x + 32.

Divide this into f(x) by long division to get a quadratic polynomial.

At worst you can use the quadratic formula to get the factors of the quadratic quotient.