Eisenstein Criterion

Eisenstein criterion

For $f\in \mathbb{Q}[x]$ where $f(x)=a_n{x}^n+\cdots +a_{1}x+a_0$, if there exists prime $p$ such that $p\nmid a_n$, $p\mid a_i$ for all $i\in \{0,\cdots ,n-1\}$ and $p^2\nmid a_0$, then $f(x)$ is irreducible over $\mathbb{Q}$.