Showing the Irreducibility of a Polynomial and "Splitting" the Field
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 $\mathbb{Q}[X]$?
93196
$x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
120627
Reducibility of polynomials modulo p
16592
Irreducible polynomial which is reducible modulo every prime
118950
Irreducibility criteria for polynomials with several variables.
76017
Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
114198
Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.
148909
Irreducible polynomials of degree 3 and 5
46648
How to prove the existence of a splitting field?
80188
There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
137610
Finding the field of fractions of a quotient of a polynomial ring.
44878
Factor $x^5+x^2+1$ into irreducible polynomials in $Z[x]$
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
112427
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it