The Bezout's theorem:
Let $C$ and $D$ be two plane curves described by equations $f(X,Y) = 0$ and $g(X,Y) = 0$, where $f$ and $g$ are nonzero polynomials of degree $m$ and $n$, respectively. Bezout’s theorem says that if all is well, then $C$ and $D$ meet in precisely $mn$ points.
Is there a use in Abstract Algebra of the Bezout's theorem? If there is what is it?