Proving certain polynomials are irreducible over $\mathbb{Z}$
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
129109
Is the set of polynomial with coefficients on $\mathbb{Q}$ enumerable?
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
155962
Are there irreducible polynomials that are partially solvable by radicals?
57884
Number of monic irreducible polynomials of prime degree $p$ over finite fields
132572
Why this polynomial is irreducible?
80188
There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$
70523
Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.
67001
Factorizing polynomials over fields other than $\mathbb{C}$
156671
Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
10627
When is $X^n-a$ is irreducible over F?
119297
Finding invertible polynomials in polynomial ring $\mathbb{Z}_{n}[x]$
114198
Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.