# Coefficient

## Multiplicative factor in a mathematical expression / From Wikipedia, the free encyclopedia

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In mathematics, a **coefficient** is a multiplicative factor involved in some term of a polynomial, a series, or an expression. It may be a number (dimensionless), in which case it is known as a **numerical factor**.[1] It may also be a constant with units of measurement, in which it is known as a **constant multiplier**.[1] In general, coefficients may be any expression (including variables such as a, b and c).[2][1] When the combination of variables and constants is not necessarily involved in a product, it may be called a *parameter*.[1]

For example, the polynomial $2x^{2}-x+3$ has coefficients 2, −1, and 3, and the powers of the variable $x$ in the polynomial $ax^{2}+bx+c$ have coefficient parameters $a$, $b$, and $c$.

The **constant coefficient**, also known as **constant term** or simply **constant** is the quantity 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 the context of differential equations, an equation can often be written as equating to zero a polynomial in the unknown functions and their derivatives. In this case, the coefficients of the differential equation are the coefficients of this polynomial, and are generally non-constant functions. A coefficient is a *constant coefficient* when it is a constant function. For avoiding confusion, the coefficient that is not attached to unknown functions and their derivative is generally called the *constant term* rather the constant coefficient. In particular, in a linear differential equation with constant coefficient, the constant term is generally not supposed to be a constant function.

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