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

Terminology[

• Root of a polynomial: Given a polynomial p(x), the x values that satisfy p(x) = 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 (sum of squares)

Theory of equations[

• Polynomial family
  • Quadratic function
  • Cubic function
  • Quartic function
  • Quintic 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[

• Additive polynomials
• Appell sequence
• Askey–Wilson polynomials
• Bell polynomials
• Bernoulli polynomials
• Bessel polynomials
• Binomial type
• Caloric polynomial
• Charlier polynomials
• Chebyshev polynomials
• Ehrhart polynomial
• Exponential polynomials
• Favard's theorem
• Fibonacci polynomials
• Hahn polynomials
• Heat polynomial — see caloric polynomial
• Heckman–Opdam polynomials
• Hermite polynomials
• Kravchuk polynomials
• Laguerre polynomials
• Laurent polynomial
• Littlewood polynomial
• Legendre polynomials
  • Spherical harmonic
• Macdonald polynomials
• Meixner polynomials
• Newton polynomial
• Orthogonal polynomials
• Orthogonal polynomials on the unit circle
• Racah polynomials
• Rook polynomial
• Schur polynomials
• Sheffer sequence
• Touchard polynomials
• Wilkinson's polynomial
• Wilson polynomials
• 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