if a polynomial p(x) is divisible by 2 polynomials (x-a) and (x-b) is it necessary that p(x) will be divisible by (x-a)(x-b)?
30685
Is $f(a)\!=\!0\!=\!f(b)\Rightarrow (x\!-\!a)(x\!-\!b)\mid f(x)\,$ true if $\,a=b?\ $ [Double Factor Theorem]
116204
Polynomial Remainder Question?
131869
How to find all polynomials P(x) such that $P(x^2-2)=P(x)^2 -2$?
124380
existence of sequence of polynomial
120627
Reducibility of polynomials modulo p
127524
how to find the remainder when a polynomial $p(x)$ is divided my another polynomial $q(x)$
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 $x-1$
139930
Find all polynomials $p$ such that $p(x^2)=p(x)p(x+1)$
41810
Should all polynomial functions from F to F (F is a field) have coefficients in F?
81063
If $p$ is a polynomial, then either $\,p(z)=z^n\,$ or $\,\max_{|z|=1}|p(z)|>1$.
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
48873
Let $K$ be a field and $f(x)\in K[X]$ be a polynomial of degree $n$. And let $F$ be its splitting field. Show that $[F:K]$ divides $n!$.
129109
Is the set of polynomial with coefficients on $\mathbb{Q}$ enumerable?
114812
Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+...+a_0$ be a complex polynomial satisfying $|p(z)| \leq 1$ for $|z|\leq 1$, then prove that $p(z)=z^n$
49121
Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
137218
Does there exist a polynomial $f(x)$ with real coefficients such that $f(x)^2$ has fewer nonzero coefficients than $f(x)$?
117761
When is $\binom{n}{k}$ divisible by $n$?