Use Eisenstein´s criterion to show that $P(x)=x^n+5x^{n-1}+3$ is irreducible.
68528
$f(x)=x^n+5x^{n-1}+3$ can't be expressed as the product of two polynomials
70523
Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.
148909
Irreducible polynomials of degree 3 and 5
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
6943
Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$
95594
Prove that a polynomial is irreducible or the field contains a $p$th root
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
2043
$X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
78549
Any prime is irreducible
132572
Why this polynomial is irreducible?
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
16592
Irreducible polynomial which is reducible modulo every prime
18336
$x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.