Forming a polynomial

Question

Form a polynomial f(x) with real coefficients having the given degree and zeros

degree 4; zeros 2 -4i -3 multiplicity 2

Answer 1

(x-2)^2 [(x-2)+4i] [(x-2)-4i] =

(x-2)^2 [ (x-2)^2 + 16] =

(x^2 - 4x + 4)( x^2 - 4x + 4 + 16) =

(x^2 -4x + 4)(x^2 - 4x + 12)