How to show that $\mathbb{C}[x,y]/\langle y^2-P(x)\rangle$ is not a UFD (unique factorization domain)?

Question

I am having trouble showing that $\mathbb{C}[x,y]/\langle y^2-P(x)\rangle$, where $P\in \mathbb{C}[x]$, $\deg P\geq 2$, is not a UFD.

I actually don't really know where to begin... I've looked for any counterexamples, i.e. a term that has two factorziations, but couldn't find one. Any help would be appreciated.