# Algebraically closed concept

Suppose $$L$$ is an extension field of $$K$$ and $$L$$ is algebraically closed. Then is it trivially true that $$\forall f(x)\in K[x],~f(x)$$ splits over $$L$$? I think the answer is yes since $$L$$ is algebraically closed means that every polynomial with coefficients in $$L$$ have a root in $$L$$ (and hence have all roots in $$L$$)

• Yes, this follows by induction on the degree of $f$, starting with one root. So there is nothing to ask in your question. – Dietrich Burde Dec 15 '18 at 12:37

Yes, the splitting field of $$f(x)\in K[x]$$ must be contained in $$L$$ since $$L$$ is algebraically closed.