Prove the quartic polynomial $x^4-20x^2+16$ is irreducible over rationals
103238
Conjugates of ${\sqrt 5 + \sqrt 6 }$ over $\mathbb{Q}$ and irreducibility of $x^4 -22x^2+1$ (for minimal polynomial)
97028
Find all irreducible monic polynomials in $\mathbb{Z}/(2)[x]$ with degree equal or less than 5
10885
Existence of irreducible polynomials over finite field
70537
Irreducible polynomials have distinct roots?
16592
Irreducible polynomial which is reducible modulo every prime
32391
Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
90612
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
31215
Irreducible cyclotomic polynomial
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
76017
Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
134726
Show the polynomial is irreducible in $\textbf Z_2$
46951
For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
81377
Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$
25290
Determine the number of irreducible monic polynomials of degree 3 in $\mathbb F_p[x]$