Show a polynomial is irreducible in $\Bbb C[x,y]$
94579
$\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
2043
$X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$
24626
Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
141792
Slick proof the determinant is an irreducible polynomial
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
74777
Solvability and reducibility of a polynomial in a "chain" of finite fields
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
103246
Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
57166
Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
86038
Family of irreducible polynomials
53012
Irreducibility of a polynomial if it has no root (Capelli)
31215
Irreducible cyclotomic polynomial
106914
Existence of Irreducible polynomials over $\mathbb{Z}$ of any given degree
147047
Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?