State Gauss's Lemma. State Eisenstein's irreducibility criterion.

(i) By considering a suitable substitution, show that the polynomial $1+X^{3}+X^{6}$ is irreducible over $\mathbb{Q}$.

(ii) By working in $\mathbb{Z}_{2}[X]$, show that the polynomial $1-X^{2}+X^{5}$ is irreducible over $\mathbb{Q}$.