query: Total degree of a product of polynomials
positive_passages.docid: 146480
positive_passages.text: Example of $\deg(fg)<\deg(f)+\deg(g)$
negative_passages.docid: 119999
negative_passages.text: A property of every real polynomial.
negative_passages.docid: 16025
negative_passages.text: Havel & Hakimi degree sequence theory
negative_passages.docid: 42265
negative_passages.text: A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
negative_passages.docid: 82295
negative_passages.text: Showing that the minimal polynomial of an $n \times n$ matrix has degree at most $n$ without using the Cayley-Hamilton Theorem
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 $\mathbb{Q}$
negative_passages.docid: 62134
negative_passages.text: Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
negative_passages.docid: 134709
negative_passages.text: Express symmetric polynomial $\prod_{i < j} (X_i+X_j)$ in terms of elementary symmetric functions
negative_passages.docid: 117743
negative_passages.text: Remainder of the polynomial
negative_passages.docid: 47443
negative_passages.text: Iterated polynomial problem
negative_passages.docid: 28658
negative_passages.text: $R$ with an upper bound for degrees of irreducibles in $R[x]$
negative_passages.docid: 36034
negative_passages.text: Degree of splitting field less than n!
negative_passages.docid: 106914
negative_passages.text: Existence of Irreducible polynomials over $\mathbb{Z}$ of any given degree
negative_passages.docid: 26728
negative_passages.text: Coefficient of $n$th cyclotomic polynomial equals $-\mu(n)$
negative_passages.docid: 46572
negative_passages.text: Degree of a splitting field is no greater than $n!$
negative_passages.docid: 70249
negative_passages.text: Irreducibility of Polynomials in $k[x,y]$
negative_passages.docid: 83036
negative_passages.text: f(g(x)) has a degree divisible by n