Polynomial of prime degree: being irreducible or having a root!
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
105679
Can $\pi$ or $e$ be a root of a polynomial with algebraic coefficients?
101882
Does this polynomial evaluate to prime number whenever $x$ is a natural number?
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
84355
Methods to see if a polynomial is irreducible
132572
Why this polynomial is irreducible?
103246
Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
35478
Polynomial $p(a) = 1$, why does it have at most 2 integer roots?
16592
Irreducible polynomial which is reducible modulo every prime
38419
Existence of Polynomial with whom product contains only prime powers
40994
How to check that a cubic polynomial is irreducible?
70249
Irreducibility of Polynomials in $k[x,y]$
70537
Irreducible polynomials have distinct roots?
60816
Irreducibility of special cyclotomic polynomial.
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime
25290
Determine the number of irreducible monic polynomials of degree 3 in $\mathbb F_p[x]$
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible