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
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
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
All one 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
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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