Why is $x - a$ a factor of $p(x) - p(a)$?
109778
Proving $(x-c)|(p(x)-p(c))$
81669
The logic of the AC Method of factoring quadratic polynomials
24107
Bijection $f:\mathcal{P}(A)\to(A\to \{0,1\})$
73375
Show that $\prod (1- P(A_n))=0$ iff $\sum P(A_n) = \infty$
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
38871
How to obtain the complete factorization of $P_n(X)=\frac{(X+i)^{2n+1} - (X-i)^{2n+1}}{2i} = 0$
57979
If $P(A \cup B \cup C) = 1$, $P(B) = 2P(A) $, $P(C) = 3P(A) $, $P(A \cap B) = P(A \cap C) = P(B \cap C) $, then $P(A) \le \frac14$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
133384
Question regarding to canonical factorization of $n!$?
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
116363
If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$
158729
Are the polynomial remainder and factor theorems equivalent?
112427
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
134348
When is $(p - 1)! + 1$ a power of $p$?
152297
Understanding quotients of $\mathbb{Q}[x]$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
108633
Why $f^{-1}(f(A)) \not= A$