I am reading this article
and would like to ask if this section is correct:
If it can, then you would have
$f(x,y) = g(x,y) * h(x,y)$,
where g and h are polynomials of degree at least one (that is, not constants). It turns out that there will necessarily be at least one complex solution $(x,y)$ to the simultaneous equations
$g(x,y) = 0$ $h(x,y) = 0$
This is known from Bezout's Theorem.
Is this true? It seems like $g(x,y) = x^2 + y^2$ and $h(x,y) = x^2 + y^2 + 1$ is an obvious counterexample.