Category

Theorems about polynomials

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binomial theorem

algebraic expansion of powers of a binomial

fundamental theorem of algebra

Every polynomial has a real or complex root

polynomial remainder theorem

rational root 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

Hilbert's basis theorem

Gauss–Lucas theorem

geometric relation between the roots of a polynomial and those of its derivative

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

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