Coefficient

In algebra, a coefficient usually refers to the factor that multiplies a term in a polynomial. A coefficient can be a constant or an expression. Below is an example of a polynomail with only one variable, x:

3x² + 4x - 15

In the above polynomial, the coefficients of the first two terms are 3 and 4 respectively, and they multiply the variable x. The -15 is just referred to as a constant since it is not multiplying any variable.

Variables are most commonly expressed using x and y, though they can be expressed using other letters or symbols, as long as it is clearly stated. Coefficients are commonly represented using a, b, and c:

ax² + bx + c

The equation above is the standard form of a quadratic equation in which x is the only variable, a and b are coefficients of the variable x, and c can be referred to as the constant coefficient.

In cases where the coefficient is an expression rather than some constant, the variables that are part of the coefficient are usually referred to as parameters. In such a case it is important to clearly distinguish which variable(s) in the polynomial are parameters. For example, in the polynomial

x² - 7xy + 12 + y

if y is a parameter, rather than the coefficient of the second term being -7, the coefficient would be -7y, and rather than the constant coefficient being 12, it would be 12 + y. Very generally, a parameter is treated as somewhat of a "constant," as they are used to define relatively constant characteristics of functions. Referring again to the standard form of a quadratic equation,

ax² + bx + c

a, b, and c, are parameters that when substituted with specific values, represents a specific quadratic equation.