$x^5+x^2+1$ is irreducible in $\mathbb{Z}[x]$
44878
Factor $x^5+x^2+1$ into irreducible polynomials in $Z[x]$
127310
Suppose $\gcd(\deg(f),\deg (g))=1$. Show that $g(x)$ is irreducible in $k(\alpha)[X]$.
65558
Irreducible in $\mathbb{Z}[\sqrt{-5}]$
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
70249
Irreducibility of Polynomials in $k[x,y]$
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
138275
Show $100+t$ is reducible in $\mathbb{Z}[[t]]$
60816
Irreducibility of special cyclotomic polynomial.
53012
Irreducibility of a polynomial if it has no root (Capelli)
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
115782
Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
158182
Let $R = \mathbb{Z} + x\mathbb{Q}[x]$. Find all the irreducibles in $R$.
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
90612
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots