Fields2
From Exampleproblems
Prove that the polynomial is irreducible: ![f(x)=x^6+30x^5-15x^3+6x-120\isin \mathbb{Z}[x]\,](/wiki/images/math/8/6/5/86565a59f5fae07db72899a80905ee75.png)
Let the ideal 
. By Eisenstein's criterion, all coefficients except the first are elements in 
, and the constant term is not an element of 
. Therefore 
is irreducible over 
.
