Basics

• Polynomial
• Coefficient
• Monomial
• Polynomial long division
• Polynomial factorization
• Rational function
• Partial fraction
• Partial fraction decomposition over R
• Vieta's formulas
• Integer-valued polynomial
• Algebraic equation

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

• Binomial theorem
• Blossom (functional)
• Root (mathematics)
• Radical (mathematics)
• 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
• Quadratic equation
• Completing the square
• Cubic function
• Quartic function
• Quintic equation
• Abel-Ruffini theorem
• Quintic function
• Bring radical
• Fundamental theorem of algebra
• Hurwitz polynomial
• Tschirnhaus transformation
• Galois theory
• Discriminant of a polynomial
• Resultant
• Elimination theory
• Gröbner basis
• 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
• Binomial type
• Caloric polynomial
• Charlier polynomials
• Chebyshev polynomials
• Ehrhart polynomial
• Fibonacci polynomials
• Hahn polynomials
• Heat polynomial — see caloric polynomial
• Hermite polynomials
• Kravchuk polynomials
• Laguerre polynomials
• Legendre polynomials
• Spherical harmonic
• Meixner polynomials
• Newton polynomial
• Orthogonal polynomials
• Racah polynomials
• Rook polynomial
• Schur polynomials
• Sheffer sequence
• Touchard polynomials
• Wilkinson's polynomial
• Wilson polynomials

Knot polynomials

• Alexander polynomial
• HOMFLY polynomial
• Jones polynomial

Algorithms

• Karatsuba multiplication
• Lenstra–Lenstra–Lovász lattice basis reduction algorithm (for polynomial factorization)
• Schönhage-Strassen algorithm