A polynomial is an algebraic expression with one or more terms, each consisting of a coefficient multiplied by a variable raised to a non-negative integer power.
Polynomials have the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀. The degree is the highest exponent. Polynomials can be classified by degree: linear (1), quadratic (2), cubic (3), quartic (4), quintic (5), etc. They model a vast range of phenomena and are fundamental in algebra, calculus, approximation theory, and numerical analysis.
Polynomials have been studied since ancient mathematics. Arab mathematician Al-Karaji (10th century) worked with polynomial expansions. Modern notation was developed by François Viète and René Descartes. The Fundamental Theorem of Algebra was proved by Carl Friedrich Gauss in 1799.