In mathematics, a coefficient is a constant multiplicative factor of a certain object. The object can be such things as a variable, a vector, a function, etc. For example, the coefficient of 9x² is 9. In some cases, the objects and the coefficients are indexed in the same way, leading to expressions such as

$a\_1\; x\_1\; +\; a\_2\; x\_2\; +\; a\_3\; x\_3\; +\; \backslash cdots$

where a_n is the coefficient of the variable x_n for each n = 1, 2, 3, …

In a polynomial P(x) of one variable x, the coefficient of x^k can be indexed by k, giving the convention that for example

$P(x)\; =\; a\_k\; x^k\; +\; \backslash cdots\; +\; a\_1\; x^1\; +\; a\_0$

For the largest k where a_k ≠ 0, a_k is called the leading coefficient of P because most often, polynomials are written from the largest power of x, downward (i.e. x⁵ + x⁴ + x² ...).

Important coefficients in mathematics include the binomial coefficients, coefficients in the statement of the binomial theorem, which can be partially found with Pascal's triangle.

See also

• degree of a polynomial
• monic polynomial

Polynomials | Mathematical terminology | Algebra

Koeffizient | Coeficiente | Coefficient | Koeficiento | Coëfficiënt | 係数 | Koeffisient | Коэффициент | Koefficient