query: Given that $p(x)$ is a polynomial of the form $x^n + a_{n-1}x^{n-1}+ ... + a_1 x + a_0$, where $a_1, a_2, ... , a_n$ are integers
positive_passages.docid: 86882
positive_passages.text: Proving Gauss' polynomial theorem (Rational Root Test)
negative_passages.docid: 33011
negative_passages.text: Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
negative_passages.docid: 129109
negative_passages.text: Is the set of polynomial with coefficients on $\mathbb{Q}$ enumerable?
negative_passages.docid: 53669
negative_passages.text: Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
negative_passages.docid: 139190
negative_passages.text: What are the coefficients of the polynomial inductively defined as $f_1=(x-2)^2\,\,\,;\,\,\,f_{n+1}=(f_n-2)^2$?
negative_passages.docid: 48977
negative_passages.text: Polynomials having as roots the sum (respectively, the product) of two algebraic elements
negative_passages.docid: 7389
negative_passages.text: Finding the limit of $\frac{Q(n)}{P(n)}$ where $Q,P$ are polynomials
negative_passages.docid: 49121
negative_passages.text: Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
negative_passages.docid: 132410
negative_passages.text: Difficult Polynomial Question
negative_passages.docid: 141983
negative_passages.text: Complex polynomial of degree $n$
negative_passages.docid: 151961
negative_passages.text: Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
negative_passages.docid: 139017
negative_passages.text: If a polynomial takes integer values at every integer, does it have integer coefficients?
negative_passages.docid: 1487
negative_passages.text: How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
negative_passages.docid: 80502
negative_passages.text: $p(x)$ divided by $x-c$ has remainder $p(c)$? [Polynomial Remainder Theorem]
negative_passages.docid: 139930
negative_passages.text: Find all polynomials $p$ such that $p(x^2)=p(x)p(x+1)$
negative_passages.docid: 95692
negative_passages.text: Factoring polynomials of the form $1+x+\cdots +x^{p-1}$ in finite field
negative_passages.docid: 124380
negative_passages.text: existence of sequence of polynomial