Prove that the polynomial $P(x) = x^{p−1} + 2x^{p−2} + 3x^{p−3} +···+ (p − 1)x + p$ is irreducible in $\mathbb Z[x].$
127205
Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
158182
Let $R = \mathbb{Z} + x\mathbb{Q}[x]$. Find all the irreducibles in $R$.
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
85459
$x^3+x+1$ irreducible over $\mathbb{F}_2$, $\theta$ root, compute powers of $\theta$
16592
Irreducible polynomial which is reducible modulo every prime
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
129834
Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
40994
How to check that a cubic polynomial is irreducible?
147047
Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
26069
Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
60816
Irreducibility of special cyclotomic polynomial.
24626
Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
114198
Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.