A coefficient is a numerical or constant factor multiplied by a variable in an algebraic term.
In the term 5x², 5 is the coefficient and x² is the variable part. Coefficients can be constants (like 5, -3, ½) or parameters (like a, b, c in ax² + bx + c). The leading coefficient is the coefficient of the term with the highest degree. Coefficients determine the scale and direction of a term's contribution to the overall expression.
The concept of coefficients has been used since ancient algebra. The term "coefficient" was introduced by François Viète in the 16th century. The modern notation, where coefficients are written as numbers before variables, was standardized by René Descartes in the 17th century. The method of undetermined coefficients was developed by Descartes and later extended by Brook Taylor.