In order to figure this out, we need to make roots into binomials:
x = 5, 4i, and -4i
This can be written as:
f(x) = (x - 5)(x + 4i)(x - 4i)
Let's take care of the imaginary numbers first:
(x + 4i)(x - 4i)
x^2 -4ix + 4ix + 16
x^2 + 16
Now we can re-insert this into our problem and solve accordingly:
f(x) = (x - 5)(x^2 + 16)
f(x) = x^3 + 16x - 5x^2 - 80
Now we can rearrange the terms in descending order to obtain our polynomial:
f(x) = x^3 - 5x^2 + 16x - 80
