Question

If a polynomial function f(x) has roots -6 square root of -3, what must be a factor of f(x)

Answer 1

If a polynomial $f(x)$ has a root $x_0$, then the polynomial is a multiple of $x-x_0$

In your case, we have $x_0=-6\sqrt{-3}$, so the polynomial is a multiple of $x-(-6\sqrt{-3})=x+6\sqrt{-3}$