Category
page 1Theorems about polynomials
binomial theorem
algebraic expansion of powers of a binomial
fundamental theorem of algebra
Every polynomial has a real or complex root
polynomial remainder theorem
theorem
rational root theorem
theorem
multinomial theorem
theorem about how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem to polynomials
Abel–Ruffini theorem
theorem that a generic equation of degree 5 or higher cannot be solved by radicals
Descartes' rule of signs
theorem
Hilbert's basis theorem
theorem
Gauss–Lucas theorem
geometric relation between the roots of a polynomial and those of its derivative
Gauss's lemma
lemma that the greatest common divisor of the coefficients is a multiplicative function
Sturm's theorem
Count of the roots of a polynomial in an interval, without computing them
factor theorem
theorem about polynomial
Lagrange's theorem
theorem in number theory
Marden's theorem
Geometric relationship between the zeros of a cubic polynomial and of its derivative
complex conjugate root theorem
theorem that complex roots of a real polynomial come in conjugate pairs
Routh–Hurwitz theorem
mathematical theorem