State Gauss's lemma and Eisenstein's irreducibility criterion. Prove that the following polynomials are irreducible in $\mathbb{Q}[x]$ :

(i) $x^{5}+5 x+5$;

(ii) $x^{3}-4 x+1$;

(iii) $x^{p-1}+x^{p-2}+\ldots+x+1$, where $p$ is any prime number.