Does $Z[x]/(3,p(x))$ equal to $Z_3[x]/(p(x))$ for all integer coefficient polynomials?
41069
Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
85525
Prove that $x^3+x+1$ splits in $Z_2[x]/(x^3+x+1)$
7199
Suppose that $P(x)$ is a polynomial of degree $n$ such that $P(k)=\dfrac{k}{k+1}$ for $k=0,1,\ldots,n$. Find the value of $P(n+1)$
138756
How to Calculate the Sum of Coefficients in a Polynomial with known Integer Roots
145152
How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$
127524
how to find the remainder when a polynomial $p(x)$ is divided my another polynomial $q(x)$
139017
If a polynomial takes integer values at every integer, does it have integer coefficients?
31216
Is the image of $\Phi_n(x) \in \mathbb{Z}[x]$ in $\mathbb{F}_q[x]$ still a cyclotomic polynomial?
116795
Easiest way to extract the coefficient of a polynomial
41810
Should all polynomial functions from F to F (F is a field) have coefficients in F?
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 $p(z)=z^n$
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
58927
Integer coefficient polynomial $p(x)$ has no integer roots of $\,p(0)$ and $p(1)$ are odd [Parity Root Test]
121986
Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
32760
Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?