Let $k$ be a field, let $n \in \mathbb{N}$, let $d \in \mathbb{N} \cup \{0\}$, and let $f \in k[x_1,\ldots,x_n]$ be homogeneous of degree $d$, meaning that every monomial of $f$ with nonzero coefficient has total degree $d$. If $a \in k^n$ satisfies $f(a)=0$, then $f(\lambda a)=0$ for every $\lambda \in k$.