$p(x)=a_0+a_1x+\ldots+a_nx^n$ is irreducible iff $a_0x^n+a_1x^{n-1}+\ldots+a_n$ is irreducible
14830
A transformation of F[x]
64878
Is this polynomial irreducible in $\mathbb{Q}$?
41486
If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
76696
Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
16035
Irreducibility of $X^{p-1} + \cdots + X+1$
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
35959
irreducibility of a polynomial over $\mathbb{F}_2$
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
41693
Use irreducible fibers to show $X$ is irreducible
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
153062
Question about irreducible Gaussian integers
11664
If $a_0+\frac{a_1}{2}+\dots + \frac{a_n}{n+1}=0$ then $a_nx^n+\dots + a_0$ has a root in $[0,1]$
86038
Family of irreducible polynomials
132572
Why this polynomial is irreducible?
2043
$X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$
95594
Prove that a polynomial is irreducible or the field contains a $p$th root