Proving the irreducibility of a polynomial based on its Galois group

Question

Suppose $f(X) \in \mathbb{Q}[X]$ is a polynomial of degree $n$. Let $K$ be the splitting field of $f(X)$ over $\mathbb{Q}$. Prove that if $Gal(K/\mathbb{Q}) \simeq S_n $, then $f(X)$ is irreducible over $\mathbb{Q}$.

How do I prove this claim? Any help will be appreciated. Thanks.