$x^p -x-1$ irreducible over $\mathbb{F}_{p}$
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
24626
Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
121301
What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?
143107
Why is $X^4 + \overline{2}$ irreducible in $\mathbb{F}_{125}[X]$?
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
127310
Suppose $\gcd(\deg(f),\deg (g))=1$. Show that $g(x)$ is irreducible in $k(\alpha)[X]$.
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
127205
Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
120627
Reducibility of polynomials modulo p
132423
Non trivial valuation over a finite extension $F/\mathbb{Q}_p$ is equivalent to the one induced by $v_p$
96087
Let $\mathbb{F}_2 \cong \mathbb{Z}/2\mathbb{Z}$. Is $x^4+x^2+1$ irreducible in $\mathbb{F}_2[x]$?
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$