a polynomial $p(x)$ is divisor of $0$ $\iff$ there is $c\in R\backslash \{0\}$ s.t. $cp(x)=0$.
17926
Zero divisor in $R[x]$
158148
Find all polynomials $P(x)$ such that $P(x^2)=P(x)^2$
117777
What are the zero divisors of $C[0,1]$?
70249
Irreducibility of Polynomials in $k[x,y]$
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 $n!$.
83337
If $A ∈M_n(C)$ is such that $(Ax,x) = 0$ for all $x ∈C^n$, then $A = 0$
139019
Polynomial satisfying $f(x) = f'(x) \cdot f''(x)$
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
121076
Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$
13083
If for a polynomial $P(k) = 2^k$ for $k = 0, 1, . . . , n$, what is $P(n+1)$?
69523
Prove that polynomial of degree $4$ with real roots cannot have $\pm 1$ as coefficients (IITJEE)
114254
Zero divisors in $A[x_1,x_2,\dots,x_r]$
134342
Find a polynomial of degree > 0 in $\mathbb Z_4[X]$ that is a unit.
147047
Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
156034
sufficient condition for a polynomial to have roots in $[0,1]$