Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b and c). When the coefficients are variables, they are often called parameters.

For example,

$2x^{2}-x+3$ , has the real coefficients 2, -1, and 3 respectively, and

$ax^{2}+bx+c$ , has coefficient parameters a, b, and c respectively- assuming x is the variable of the equation.

The constant coefficient is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the real coefficient 3 and the parameter represented by c.

Similarly, the coefficient attached to the highest multiplicity of the variable in a polynomial is referred to as the leading coefficient. For example in the expressions above, the leading coefficients are 2 and the parameter represented by a.

The binomial coefficients occur in the expanded form of $(x+y)^{n}$ , and are tabulated in Pascal's triangle.