How do you write a polynomial function of least degree with integral coefficients that has the given zeros?

Question

1. 3/5, -2/3, -3

2. -3 - 2i, -3 + 2i, 3 + √6

Answer 1

1) f(x) = (5x-3)(3x+2)(x-3)

2)

[(x + 3) - 2i][ (x+3) + 2i] [ (x-3) + sqrt(6) ] [ (x-3) - sqrt(6)] =

[ (x+3)^2 + 4] [ (x-3)^2 - 6]

[ x^2 + 6x 13][ x^2 - 6x + 3]