List of polynomial 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

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

Tschirnhaus transformation

Galois theory

Discriminant of a polynomial

Resultant

Elimination theory

Gröbner basis

Regular chain

Triangular decomposition

Sturm's theorem

Descartes' rule of signs

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

Additive polynomials

Appell sequence

Askey–Wilson polynomials

Bell polynomials

Bernoulli polynomials

Bernstein polynomial

Bessel polynomials

Binomial type

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