2004-75.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	75	IB 2004 Groups, Rings and Modules	4.I.2F	2004

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.