Proving that $I+x$ is irreducible in $R/I$, where $R=k[x,y,z]$ and $I=\langle x^2-yz\rangle$

Question

Let $K$ be a field and $I=\langle x^2-yz\rangle$. I am trying to prove that $R=K[x,y,z]/\langle x^2-yz\rangle$ is not a UFD.

My idea is that $(I+y)(I+z)=(I+x)^2$. But I am unable to prove that $I+x, I+y$ and $I+z$ are irreducibles in $R$.

How to prove their irreducibility?