Show that $x^p - m$ is irreducible for prime $p$ and $m \in \mathbb{Q^{\times}}\setminus \left(\mathbb{Q^{\times}}\right)^p$
18336
$x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
64878
Is this polynomial irreducible in $\mathbb{Q}$?
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
110662
Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
16592
Irreducible polynomial which is reducible modulo every prime
4105
Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
60816
Irreducibility of special cyclotomic polynomial.
90612
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
10821
Using Eisenstein criterion show that $x^3+x^2-2x-1$ is irreducible?
112427
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
120627
Reducibility of polynomials modulo p
41693
Use irreducible fibers to show $X$ is irreducible