Remark. special case that $A$ is finite [2203]
Remark. special case that $A$ is finite [2203]
If $A$ is a finite subset of $F[x]$, say $A = \{ f_{1}(x), \dots, f_{n}(x) \}$. Then a field extension $K$ of $F$ is a splitting field for $A$ over $F$ if and only if $K$ is a splitting field for $$ f(x) = f_{1}(x) f_{2}(x) \cdots f_{n}(x) \in F[x]. $$