Prove that there is no polynomial $P(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_0 $
10514
Proof that no polynomial with integer coefficients can only produce primes
127547
Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
155575
Proving a polynomial $f(x)$ composite for infinitely many $x$
14836
A polynomial sequence
39346
Let $R= \mathbb{Q}[x^2 ,x^3 ]$, the set of all polynomials over $\mathbb{Q}$ with no $x$ term. Show that the $\gcd$ of $x^5$ and $x^6$ does not exist
13083
If for a polynomial $P(k) = 2^k$ for $k = 0, 1, . . . , n$, what is $P(n+1)$?
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 $P(n+1)$
147952
Why can we prove mathematically that a formula to solve an (n+5) order polynomial does not exist?
2408
Show that a polynomial has at least one positive solution/root.
40502
The Degree of Zero Polynomial.
88466
Show that polynomial $X^{n+1}-aX^n+aX-1$ has only roots of module $1$
58927
Integer coefficient polynomial $p(x)$ has no integer roots of $\,p(0)$ and $p(1)$ are odd [Parity Root Test]
33099
If $f$ is an entire function where every power series expansion has at least one 0 term, show it is a polynomial
104965
Find $n$ such that polynomial is divisible
147047
Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
132165
"Polynomials" with non-integer exponents
124380
existence of sequence of polynomial