Find a polynomial with integer coefficients that satisfie Q has degree 3 and zeros -3 and 1 + i.

Question

Finding a polynomial function with the given conditions

Answer 1

Complex zeroes must be in pairs so zero 1+i must be matched with 1-i. These two zeroes create a quadratic: (x-1)²+1=x²-2x+2 (because (x-1-i)(x-1+i)=(x-1)²+1).

So the polynomial is a(x+3)(x²-2x+2)=a(x³+x²-4x+6) where a is a constant.