This is my first post on here so let me begin by giving a hearty Hello to all!

On to the problem:

Find a nth-degree polynomial function w/real coefficients given the following conditions:

n=3 | 4 and 2i are zeros | f(2)=-16

I begin by creating a function from the zeros that are given and working backwards. Like this:

I included (x+2i) as well because if complex numbers appear in the zeros of the polynomial then they also have the complex conjugate.

Then I expand like so:

So now I just need to find ... I think I am suppose to plug 3 in for , since it is a 3rd degree polynomial, and then solve. I am not sure though. Any help would be appreciated.