$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
94579
$\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
46891
Irreducibility of reciprocal polynomials
158182
Let $R = \mathbb{Z} + x\mathbb{Q}[x]$. Find all the irreducibles in $R$.
8977
Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible
31215
Irreducible cyclotomic polynomial
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
127205
Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
4105
Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
32391
Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.
118950
Irreducibility criteria for polynomials with several variables.
70537
Irreducible polynomials have distinct roots?
154845
Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
10627
When is $X^n-a$ is irreducible over F?