How to find a cubic function given roots - 3 and 2i

A cubic function has three roots, so in factored form it would look like

f (x) = () () ()

We know one of the roots is - 3, so one of the factors is (x+3)

f (x) = (x+3) () ()

Since the root 2i is given the root - 2i also has to exist.

f (x) = (x + 3) (x - 2i) (x + 2i)

If you want to simplify, it becomes

f (x) = (x + 3) (x^2 + 4)

f (x) = x^3 + 3x^2 + 4x + 12