In an algebraic equation, a coefficient is simply a multiplicative factor. In the majority of cases, the coefficient is the numerical part (most often a constant) of the equation. Thus, it is called a numerical coefficient. For example, in 3x = 6, the coefficient is 3; in -3x = 6, the coefficient is -3, as the coefficient takes on the sign of the operation. Terms such as xy may not appear to have a numerical coefficient, but it is 1—a number that is not written, but assumed.

Coefficients do not have to be just numbers: In the equation 5x³y, the coefficient of x³y is 5. But in addition, the coefficient of x is 5x²y, and the coefficient of y is 5x³. Coefficients are also seen in functions; for example, in the function f(x) = 2x, the 2 is the coefficient.

A 1621 Latin edition of Greek mathematician Diophan-tus’s Arithmetica.