Prove that $x^{5}-x+a$ is an irreducible polynomial
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
12166
How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$?
7858
Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
97028
Find all irreducible monic polynomials in $\mathbb{Z}/(2)[x]$ with degree equal or less than 5
102432
Irreducible polynomial of degree $8$
116363
If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$
151961
Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
79564
Algorithm to find the irreducible polynomial
70249
Irreducibility of Polynomials in $k[x,y]$
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
130027
Give a direct proof of the fact that $a^2-5a+6$ is even for any $a \in \mathbb Z$
141792
Slick proof the determinant is an irreducible polynomial
49121
Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?