$f\in K[t]$ is irreducible if and only if $G$ $(\Gamma(L:K))$ acts transitively on the roots of $f$.
137233
$f$ is irreducible $\iff$ $G$ act transitively on the roots
65558
Irreducible in $\mathbb{Z}[\sqrt{-5}]$
8977
Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible
46951
For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
41693
Use irreducible fibers to show $X$ is irreducible
111935
Irreducible but not prime
146572
Prove that between any two roots of $f$ there exists at least one root of $g$
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
138275
Show $100+t$ is reducible in $\mathbb{Z}[[t]]$
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
142093
The closure of an irreducible subset of an irreducible space is irreducible.
40114
Factor into irreducibles in $\mathbb{Z}[\omega]$ (Eisenstein Integers).
114762
Prove that $f(x)$ is irreducible iff its reciprocal polynomial $f^*(x)$ is irreducible.
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
31215
Irreducible cyclotomic polynomial
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
48093
Irreducible polynomial in field extension