Show that there exist a polynomial $q_n(x) \in \mathbb Q[x] $ satisfying $p_n(x)=(x-1)^2q_n(x)$.
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
141983
Complex polynomial of degree $n$
155575
Proving a polynomial $f(x)$ composite for infinitely many $x$
121304
Is the set of polynomials of degree less than or equal to $n$ closed?
134342
Find a polynomial of degree > 0 in $\mathbb Z_4[X]$ that is a unit.
82204
Prove $ \lim_{n\to\infty}\sqrt[n]{p(n)}=1 $ for polynomial
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
124380
existence of sequence of polynomial
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 $P(n+1)$
7389
Finding the limit of $\frac{Q(n)}{P(n)}$ where $Q,P$ are polynomials
149661
For $n=pq$, show that there exist $\alpha, \beta \in Z_n^*$ such that $\alpha, \beta \notin (Z_n^*)^2$ and $\alpha \cdot \beta \notin (Z_n^*)^2$.
103340
Show that this entire function is polynomial.
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
112205
Which of the following polynomials are subspaces of $\mathbb{P}_n$ for an appropriate value of n?
43792
Find polynomials such that $(x-16)p(2x)=16(x-1)p(x)$
152982
Show that the range of $p(z)e^{q(z)}$ for nonconstant polynomials $p$ and $q$ is all of $\mathbb{C}$.
133101
Number of solutions of $P(x)=e^{ax}$ if $P$ is a polynomial