Conditions of polynomial irreducibility
101637
Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
155962
Are there irreducible polynomials that are partially solvable by radicals?
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
91356
Irreducibility of an infinite sequence of polynomials
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
57884
Number of monic irreducible polynomials of prime degree $p$ over finite fields
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
52528
Showing that minimal polynomial has the same irreducible factors as characteristic polynomial
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
76017
Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
93196
$x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$
114198
Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.