Let $F$ be a field and $\langle a_1,...,a_n \rangle \subset F$.
Then given a non-zero polynomial $f \in F[X_1,...,X_n]$ is it true that if $f(a_1,...,a_n)=0$ then $(X_i - a_i)$ divides $f$ for some $i\leq n$?
Let $F$ be a field and $\langle a_1,...,a_n \rangle \subset F$.
Then given a non-zero polynomial $f \in F[X_1,...,X_n]$ is it true that if $f(a_1,...,a_n)=0$ then $(X_i - a_i)$ divides $f$ for some $i\leq n$?