$x^2+y^2-1$ is irreducible in $\mathbb{Q}[x,y]$.
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
8164
Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
26069
Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
10627
When is $X^n-a$ is irreducible over F?
4000
If every polynomial of degree 2 is reducible then $K$ is algebraically closed?
40994
How to check that a cubic polynomial is irreducible?
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
118950
Irreducibility criteria for polynomials with several variables.
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
127310
Suppose $\gcd(\deg(f),\deg (g))=1$. Show that $g(x)$ is irreducible in $k(\alpha)[X]$.
31215
Irreducible cyclotomic polynomial
157031
Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2[x]$