write a polynomial function of least degree with integral coefficients whose zeros include 4 and 2i

Answer 1

If (x - 2i ) then also the complex conjugate (x+2i) must be a factor. Then of course (x-4) so:
(x-2i)(x+2i)(x-4)
=(x^2+4)(x-4)
=x^3 - 4 x^2 + 4 x -16