Prove $p(x) = x^3+x+1\in\mathbb{Z}_5[x]$ is irreducible over $\mathbb{Z}_5$
40994
How to check that a cubic polynomial is irreducible?
26069
Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
151961
Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
4105
Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
90612
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
48093
Irreducible polynomial in field extension
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
7858
Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
80188
There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
53012
Irreducibility of a polynomial if it has no root (Capelli)
53244
Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
46292
Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$