Irreducibility of $ X^{p^{n}}-a$
95594
Prove that a polynomial is irreducible or the field contains a $p$th root
24626
Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
81377
Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$
46292
Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
63605
Irreducible polynomials and affine variety
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
11962
Irreducibility check for polynomials not satisfying Eisenstein Criterion.
7858
Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
102422
Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$
41693
Use irreducible fibers to show $X$ is irreducible
78549
Any prime is irreducible
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
8164
Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
90612
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots