query: Prove that $f(x,y)$ is a polynomial if $f(-,y)$ and $f(x,-)$ are
positive_passages.docid: 87331
positive_passages.text: Real polynomial in two variables
negative_passages.docid: 48873
negative_passages.text: 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 $n!$.
negative_passages.docid: 103340
negative_passages.text: Show that this entire function is polynomial.
negative_passages.docid: 53244
negative_passages.text: Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
negative_passages.docid: 114146
negative_passages.text: Polynomial in $n$ variables
negative_passages.docid: 112334
negative_passages.text: Real roots of a polynomial of real co-efficients , with the co-efficients of $x^2 , x$ and the constant term all $1$
negative_passages.docid: 1962
negative_passages.text: Polynomial $P(a)=b,P(b)=c,P(c)=a$
negative_passages.docid: 127056
negative_passages.text: How to prove that a polynomial of degree $n$ has at most $n$ roots?
negative_passages.docid: 131869
negative_passages.text: How to find all polynomials P(x) such that $P(x^2-2)=P(x)^2 -2$?
negative_passages.docid: 55119
negative_passages.text: Proof that the coefficients of a polynomial are real
negative_passages.docid: 111569
negative_passages.text: Property of a polynomial with no positive real roots
negative_passages.docid: 114762
negative_passages.text: Prove that $f(x)$ is irreducible iff its reciprocal polynomial $f^*(x)$ is irreducible.
negative_passages.docid: 41810
negative_passages.text: Should all polynomial functions from F to F (F is a field) have coefficients in F?
negative_passages.docid: 154507
negative_passages.text: If all the roots of a polynomial P(z) have negative real parts, prove that all the roots of P'(z) also have negative real parts
negative_passages.docid: 73419
negative_passages.text: For $f$ entire and $\{f(kz) : k \in \mathbb{C}\}$ a normal family, prove that $f$ is a polynomial.
negative_passages.docid: 127547
negative_passages.text: Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
negative_passages.docid: 116856
negative_passages.text: Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$