Must an irreducible polynomial over a field extension divide the irreducible polynomial over the subfield?
100162
Minimal polynomial over an extension field divides the minimal polynomial over the base field
155962
Are there irreducible polynomials that are partially solvable by radicals?
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
74777
Solvability and reducibility of a polynomial in a "chain" of finite fields
49121
Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
154373
How many irreducible monic quadratic polynomials are there in $\mathbb{F}_p[X]$?
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
7452
Splitting of primes in the compositum of fields
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
8164
Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?
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 $n!$.
38209
How often must an irreducible polynomial take a prime value?