Question

Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.)

Answer 1

4,4-4i

Answer 2

Since it's going to be with real coefficients, one of the zeros is going to be the opposite of (4-4i) which will be (-4+4i)
so your equation, using your given zeros, will now be
f(x)=(x-4)(x-4+4i)(x+4-4i)
Now distribute. I recommend distributing the last two first
so now you have
f(x)=(x-4)(x²-16-16i²)
Now just finish distributing and there's your answer.
Remember i²=-1, so plug it in wherever it's necessary. :D

Answer 3

i actually gathered the answer by using a kind of reverse quadratic formula but thank you. i wasnt sure of the proper method.

Answer 4

lol np :D have fun.