How can the root of an irreducible polynomial exist?
121301
What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it
46891
Irreducibility of reciprocal polynomials
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
86038
Family of irreducible polynomials
85459
$x^3+x+1$ irreducible over $\mathbb{F}_2$, $\theta$ root, compute powers of $\theta$
35478
Polynomial $p(a) = 1$, why does it have at most 2 integer roots?
134726
Show the polynomial is irreducible in $\textbf Z_2$
60816
Irreducibility of special cyclotomic polynomial.
64878
Is this polynomial irreducible in $\mathbb{Q}$?
53012
Irreducibility of a polynomial if it has no root (Capelli)
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
105679
Can $\pi$ or $e$ be a root of a polynomial with algebraic coefficients?
155245
root of an odd degree polynomial
74777
Solvability and reducibility of a polynomial in a "chain" of finite fields
157266
Can a nonzero polynomial evaluate to the zero function in a suitable infinite ring of char 0?
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)