# List of polynomial topics

This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics.

## Terminology

* Degree: The maximum exponents among the monomials.
* Factor: An expression being multiplied.
* Linear factor: A factor of degree one.
* Coefficient: An expression multiplying one of the monomials of the polynomial.
* Root (or zero) of a polynomial: Given a polynomial p(x), the x values that satisfy p(x) = 0 are called roots (or zeroes) of the polynomial p.
* Graphing
** End behaviour –
** Concavity –
** Orientation –
** Tangency point –
** Inflection point – Point where concavity changes.

## Basics

* Polynomial
* Coefficient
* Monomial
* Polynomial long division
* Synthetic division
* Polynomial factorization
* Rational function
* Partial fraction
** Partial fraction decomposition over R
* Vieta's formulas
* Integer-valued polynomial
* Algebraic equation
* Factor theorem
* Polynomial remainder theorem

### Elementary abstract algebra

    See also Theory of equations below.
* Polynomial ring
* Greatest common divisior of two polynomials
* Symmetric function
* Homogeneous polynomial
* Polynomial SOS (sum of squares)

## Theory of equations

* Polynomial family
** Quadratic function
** Cubic function
** Quartic function
** Quintic function
** Sextic function
** Septic function
** Octic function
* Completing the square
* Abel–Ruffini theorem
* Bring radical
* Binomial theorem
* Blossom (functional)
* Root of a function
* nth root (radical)
** Surd
** Square root
** Methods of computing square roots
** Cube root
** Root of unity
** Constructible number
** Complex conjugate root theorem
* Algebraic element
* Horner scheme
* Rational root theorem
* Gauss's lemma (polynomial)
* Irreducible polynomial
** Eisenstein's criterion
** Primitive polynomial
* Fundamental theorem of algebra
* Hurwitz polynomial
* Polynomial transformation
* Tschirnhaus transformation
* Galois theory
* Discriminant of a polynomial
** Resultant
* Elimination theory
** Gröbner basis
** Regular chain
** Triangular decomposition
* Sturm's theorem
* Descartes' rule of signs
* Carlitz–Wan conjecture
* Polynomial decomposition, factorization under functional composition

## Calculus with polynomials

* Delta operator
* Bernstein–Sato polynomial

## Polynomial interpolation

* Lagrange polynomial
* Runge's phenomenon
* Spline (mathematics)

## Weierstrass approximation theorem

* Bernstein polynomial

## Linear algebra

* Characteristic polynomial
* Minimal polynomial
* Invariant polynomial

## Named polynomials and polynomial sequences

* Abel polynomials
* Actuarial polynomials
* Additive polynomials
* All one polynomials
* Appell sequence
* Askey–Wilson polynomials
* Bell polynomials
* Bernoulli polynomials
* Bernstein polynomial
* Bessel polynomials
* Binomial type
* Brahmagupta polynomials
* Caloric polynomial
* Charlier polynomials
* Chebyshev polynomials
* Chihara–Ismail polynomials
* Cyclotomic polynomials
* Dickson polynomial
* Ehrhart polynomial
* Exponential polynomials
* Favard's theorem
* Fibonacci polynomials
* Gegenbauer polynomials
* Hahn polynomials
* Hall–Littlewood polynomials
* Heat polynomial — see caloric polynomial
* Heckman–Opdam polynomials
* Hermite polynomials
* Hurwitz polynomial
* Jack function
* Jacobi polynomials
* Koornwinder polynomials
* Kostka polynomial
* Kravchuk polynomials
* Laguerre polynomials
* Laurent polynomial
* Linearised polynomial
* Littlewood polynomial
* Legendre polynomials
* Associated Legendre polynomials
** Spherical harmonic
* Lucas polynomials
* Macdonald polynomials
* Meixner polynomials
* Necklace polynomial
* Newton polynomial
* Orthogonal polynomials
* Orthogonal polynomials on the unit circle
* Permutation polynomial
* Racah polynomials
* Rogers polynomials
* Rogers–Szegő polynomials
* Rook polynomial
* Schur polynomials
* Shapiro polynomials
* Sheffer sequence
* Spread polynomials
* Tricomi–Carlitz polynomials
* Touchard polynomials
* Wilkinson's polynomial
* Wilson polynomials
* Zernike polynomials
** Pseudo-Zernike polynomials

## Knot polynomials

* Alexander polynomial
* HOMFLY polynomial
* Jones polynomial

## Algorithms

* Karatsuba multiplication
* Lenstra–Lenstra–Lovász lattice basis reduction algorithm (for polynomial factorization)
* Lindsey–Fox algorithm
* Schönhage–Strassen algorithm

## Other

Polynomial mapping