Show that $x^2 +1$ is irreducible in $\mathbb{R}[x]$, but it has roots in $\mathbb{R}[x]\space/\space(x^2 +1) \cong \mathbb{C}$
105141
$\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
121076
Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$
119702
Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
20612
Is fibre product of varieties irreducible (integral)?
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
132572
Why this polynomial is irreducible?
90612
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
26069
Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
20790
What are irreducibles in the ring $R$ of entire functions?
70249
Irreducibility of Polynomials in $k[x,y]$
88466
Show that polynomial $X^{n+1}-aX^n+aX-1$ has only roots of module $1$
140808
Problem on Galois theory and irreducible polynomial