Show that in ℝ[x], no polynomial of odd degree > 1 is irreducible.
13981
Proof that every polynomial of odd degree has one real root
40014
A polynomial that is zero on an open set
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
156034
sufficient condition for a polynomial to have roots in $[0,1]$
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$
97028
Find all irreducible monic polynomials in $\mathbb{Z}/(2)[x]$ with degree equal or less than 5
102432
Irreducible polynomial of degree $8$
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
111569
Property of a polynomial with no positive real roots
155245
root of an odd degree polynomial
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
80188
There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
155962
Are there irreducible polynomials that are partially solvable by radicals?
46891
Irreducibility of reciprocal polynomials
18336
$x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
132572
Why this polynomial is irreducible?
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$