2018-34.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	34	IB 2018 Groups, Rings and Modules	Paper 3, Section II, G	2018

(a) State Gauss's Lemma.

(b) State and prove Eisenstein's criterion for the irreducibility of a polynomial.

(c) Determine whether or not the polynomial

$$f(X)=2 X^{3}+19 X^{2}-54 X+3$$

is irreducible over $\mathbb{Q}$.