1. ## Is this right?

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?

2. I get $x^5-6x^4+\color{blue}10x^3-8x^2$.