Find a polynomial function with integer coefficients that has the given zeros:

0, 0, 4, 1 + i

My work:

f(x) = (x - 0) (x - 0) (x - 4) (x - 1 - i)

x^2 (x - 4) multiply (x - (1 + i)) (x - (1 - i))

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

x^5 - 6x^4 + 3x^3 - 4x^2

So I'm not sure if this is correct?