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In mathematics, a **coefficient** is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as a, b and c).^{[1]} When the coefficients are themselves variables, they may also be called parameters.

For example, the polynomial has coefficients 2, −1, and 3, and the powers of the variable in the polynomial have coefficient parameters , , and .

The **constant coefficient** is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the number 3 and the parameter *c*, respectively.
The coefficient attached to the highest degree 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 *a*, respectively.

In mathematics, a **coefficient** is a multiplicative factor in some term of a polynomial, a series, or any expression. For example, in the polynomial

In many scenarios, coefficients are numbers (as is the case for each term of the previous example), although they could be parameters of the problem—or any expression in these parameters. In such a case, one must clearly distinguish between symbols representing variables and symbols representing parameters. Following René Descartes, the variables are often denoted by x, y, ..., and the parameters by a, b, c, ..., but this is not always the case. For example, if y is considered a parameter in the above expression, then the coefficient of x would be −3*y*, and the constant coefficient (with respect to x) would be 1.5 + *y*.

When one writes

Any polynomial in a single variable x can be written as

In linear algebra, a system of linear equations is frequently represented by its coefficient matrix. For example, the system of equations

The **leading entry** (sometimes *leading coefficient*^{[citation needed]}) of a row in a matrix is the first nonzero entry in that row. So, for example, in the matrix

Though coefficients are frequently viewed as constants in elementary algebra, they can also be viewed as variables as the context broadens. For example, the coordinates of a vector in a vector space with basis are the coefficients of the basis vectors in the expression

**^**Weisstein, Eric W. "Coefficient".*mathworld.wolfram.com*. Retrieved 2020-08-15.

- Sabah Al-hadad and C.H. Scott (1979)
*College Algebra with Applications*, page 42, Winthrop Publishers, Cambridge Massachusetts ISBN 0-87626-140-3 . - Gordon Fuller, Walter L Wilson, Henry C Miller, (1982)
*College Algebra*, 5th edition, page 24, Brooks/Cole Publishing, Monterey California ISBN 0-534-01138-1 .