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 of a polynomial: Given a polynomial p, the x values that satisfy p = 0 are called roots 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

• Polynomial ring
• Greatest common divisior of two polynomials
• Symmetric function
• Homogeneous polynomial
• Polynomial SOS

  [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
• Root of a function
• nth root
• * 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
• 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

  [Weierstrass approximation theorem]

• Bernstein polynomial

  [Linear algebra]

• Characteristic polynomial
• Minimal polynomial
• Invariant polynomial

  Named polynomials and [polynomial sequence]s

• 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 polynomial]s

• Alexander polynomial
• HOMFLY polynomial
• Jones polynomial

  [Algorithm]s

• Karatsuba multiplication
• Lenstra–Lenstra–Lovász lattice basis reduction algorithm
• Lindsey–Fox algorithm
• Schönhage–Strassen algorithm