How could I prove that $x^2+1$ and $x^4+1$ are irreductible over $\mathbb{Z}/2 \mathbb{Z}$ and $\mathbb{Z}/3 \mathbb{Z}$?
37068
How could it possible to factorise $x^8-1$ in product of irreducibles in the rings $(\mathbb{Z}/2\mathbb{Z})[x]$ and $(\mathbb{Z}/3\mathbb{Z})[x]$?
26069
Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
102422
Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
33781
Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
96087
Let $\mathbb{F}_2 \cong \mathbb{Z}/2\mathbb{Z}$. Is $x^4+x^2+1$ irreducible in $\mathbb{F}_2[x]$?
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
70523
Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
48093
Irreducible polynomial in field extension
127205
Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
118950
Irreducibility criteria for polynomials with several variables.
35959
irreducibility of a polynomial over $\mathbb{F}_2$
61987
$x^2+1=0$ in $\mathbb{Z}_7$