# Gauss' Lemma

## Gauss' Lemma

If $f(x)$ is a polynomial with integer coefficients with deg $f(x) \geq 1$. Then $f(x)$ is irreducible over $\Q \iff$ when $f(x) = g(x)h(x)$ with $g(x), h(x) \in \Z [x]$, then deg $g(x) = 0$ or deg $h(x) = 0$.