Let $\displaystyle f(x,y)$ and $\displaystyle g(x,y)$ be polynomials with real coefficients. Show that if $\displaystyle f,g$ have no common factors, then the curves $\displaystyle f(x,y)=0$ and $\displaystyle g(x,y)=0$ will intersect in at most finitely

many points. ("at most finitely many" means either none or finitely many!)