Elementary proof of existence of irreducible polynomials of arbitrary degree in $K[X]$ for $K$ a field
80188
There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
16592
Irreducible polynomial which is reducible modulo every prime
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 $k=0, \dots, n$.
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
99756
Squarefree polynomials over finite fields
118916
How do I prove that a polynomial F[x] of degree n has at most n roots
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
31142
Why does $K \leadsto K(X)$ preserve the degree of field extensions?
148909
Irreducible polynomials of degree 3 and 5
102422
Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$
55858
Irreducible polynomial is always separable in char 0 field
48873
Let $K$ be a field and $f(x)\in K[X]$ be a polynomial of degree $n$. And let $F$ be its splitting field. Show that $[F:K]$ divides $n!$.
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
11962
Irreducibility check for polynomials not satisfying Eisenstein Criterion.
119297
Finding invertible polynomials in polynomial ring $\mathbb{Z}_{n}[x]$
141792
Slick proof the determinant is an irreducible polynomial
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$