Prove that the irreducible polynomial for $\sqrt2+\sqrt3$ over $\mathbb{Q}$ is reducible modulo $p$ for every prime $p$
70523
Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
26069
Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
132572
Why this polynomial is irreducible?
79564
Algorithm to find the irreducible polynomial
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
24626
Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
32391
Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.
4000
If every polynomial of degree 2 is reducible then $K$ is algebraically closed?
93291
Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
10266
Minimal polynomial reducible modulo every prime $p$
16035
Irreducibility of $X^{p-1} + \cdots + X+1$
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible