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 Gottlieb 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 Remez algorithm (to find best approximating polynomials) Schönhage–Strassen algorithm
Other Polynomial mapping