Let $f(x)=a_0x^n+a_1x^{n-1}+\dots+a_n$, $g(x)=b_0x^m+b_1x^{m-1}+\dots+b_m$, with coefficients in a field. Prove that $a_0^mb_m^n$ divides the resultant of $f(x)$ and $g(x)$.
I have written the resultant as a determinant, I see that $a_0^mb_m^n$ is the product over the main diagonal, but I don't know how to proceed further. I tried Laplace expansion but it didn't help.