Problem: Prove that $x^4 + 10x^2 + 5$ is irreducible over $\mathbb{Q} $.
Solution: We will use Eisenstein's criterion for irreducibility of polynomial. Take $p=5$. Note that $p \mid 5,~ p \mid 10$ but $p^2$ does not divide $5$. Hence, by the Eisenstein's criterion, the given polynomial is irreducible over $\mathbb{Q} $.