$f$ irreducible plus $(x-\alpha)| f$ and $(x-\alpha)|f'$ implies $f|f'$
25891
GCD in polynomial rings with coefficients in a field extension
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
127310
Suppose $\gcd(\deg(f),\deg (g))=1$. Show that $g(x)$ is irreducible in $k(\alpha)[X]$.
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
28399
Showing $f$ is constant
75653
Prove that $|f ''|\ge 4$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
41505
Transcendental Extensions. $F(\alpha)$ isomorphic to $F(x)$
85096
Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.
115782
Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
71857
Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $
115636
Show that $f$ is either injective or a constant function.
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
137233
$f$ is irreducible $\iff$ $G$ act transitively on the roots
45602
Show that is $\int_A f$ exists, then so does $\int_A |f|$
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$