f(x)=x^3-6x^2+16x-96; zero:4i what are the remaining zeros

Question

use the given zero to find the remaining zeros of the function

Answer 1

Given 4i as a zero, -4i must also be a zero, so (x²+16) must be a factor (product of x-4i and x+4i).

Now divide x²+16 into the polynomial:

            x-6                  

x²+16 ) x³-6x²+16x-96

            x³         16x

               -6x²        -96

              -6x²         -96

f(x)=(x-6)(x+4i)(x-4i).