resultant

《incompressible-fluid-equations》 · 第 35–36 页 · Chapter 3，Lemma 3.6

This determinant is called the resultant $R(f,g)$ of $f$ and $g$ with respect to $z$. Two polynomials $f$ and $g$ in one variable over a field $K$ will have a common factor if and only if the resultant $R(f,g)=0$.