Let $f:R\to R$ a polynomial from degree $n\in N$, such that $f(x) \ge 0$ for all $x \in R$. Explain why n is an even number.
127547
Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
39230
Even function has even sequences of polynomials converging uniformly?
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
148788
Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
26728
Coefficient of $n$th cyclotomic polynomial equals $-\mu(n)$
146665
Prove that $f(x)=8$ for all natural numbers $x\ge{8}$
3599
show that if ${a_n} \to a$, and $a>0$, then $\exists N$ such that $a_n>0$ for $n \ge N$.
10564
$f$ be a smooth function on real line , $f(0)=0$ , $f(x)>0, \forall x \ne 0$ and any $f^{(n)}(0)=0$ ; is $\sqrt f$ smooth?
43870
Explain why a composite function in which g(x) is any function, is applied to the output of any even function h(x) , f(x) is always even.
155642
Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
27540
A polynomial can not have infinite number of constant values
63590
Let $g$ be a function from $(0, 1)$ to $\mathbb{R}$ and $\int_0^1 g^2(x)dx$ finite. Does this imply that $\int_0^1 g(x)dx$ is finite?
152223
If $0<r<1$ show that $r^n$ goes to $0$ as $n$ goes to 1.
65619
Does $f^{(n)} = 0$ imply that complex $f$ is a polynomial?
38568
Finding the number of zeros of $f(z) = z^n$ if $|f(z)| < 1 $ for all $z$ with $|z|=1$.
75653
Prove that $|f ''|\ge 4$
107133
Let f(x) be a polynomial satisfying $\lim_{x \to\infty} \frac{x^4f(x)}{x^8+1}=3,$ $f(2)=5 $ and $f(3)=10$, $f(-1)=2$ and $f(-6)=37$