En matemáticas, un coeficiente es un factor vinculado a un monomio. Dado un divisor del monomio, el coeficiente es el cociente del monomio por el divisor. Así el monomio es el producto del coeficiente y el divisor. Los diferentes coeficientes dependerán de la factorización del monomio. Un coeficiente numérico es un factor constante de un objeto específico. Por ejemplo, en la expresión 9x2, el coeficiente de x2 es 9. En álgebra elemental, coeficientes numéricos de términos semejantes se agrupan para simplificar las expresiones algebraicas.. El objeto puede ser cosas tales como una variable, un vector, una función, etc. En algunos casos, los objetos y los coeficientes están ordenados de la misma manera, dando lugar a expresiones tales como: donde an es el coeficiente de la variable xn para cada n = 1, 2, 3, … En un polinomio P(x) de una variable x, el coeficiente de xk puede ordenar por k, dando por ejemplo: Para el mayor valor de k, donde ak ≠ 0, ak se denomina primer coeficiente de P, ya que la mayor parte de las veces, los polinomios se escriben a partir de la izquierda, con la mayor potencia de x. Así, por ejemplo, el primer coeficiente del polinomio: es 4. Los coeficientes de los polinonios también pueden estar en otro orden: 9x2+9+6 y debe ser a0 ≠ 0 y a0 es el primer coeficiente de Q.

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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 in any case does not involve any variable of the expression. For instance in the first two terms respectively have the coefficients 7 and −3. The third term 1.5 is a constant. The final term does not have any explicitly written coefficient, but is considered to have coefficient 1, since multiplying by that factor would not change the term. Often coefficients are numbers as in this example, although they could be parameters of the problem or any expression in these parameters. In such a case one must clarify which symbols represent variables and which ones represent parameters. Following Descartes, the variables are often denoted by x, y, ..., and the parameters by a, b, c, ..., but it is not always the case. For example, if y is considered as a parameter in the above expression, the coefficient of x is −3y, and the constant coefficient is 1.5 + y. When one writes , it is generally supposed that x is the only variable and that a, b and c are parameters; thus the constant coefficient is c in this case. Similarly, any polynomial in one variable x can be written as for some integer , where are coefficients; to allow this kind of expression in all cases one must allow introducing terms with 0 as coefficient.For the largest with (if any), is called the leading coefficient of the polynomial. So for example the leading coefficient of the polynomial is 4. Specific coefficients arise in mathematical identities, such as the binomial theorem which involves binomial coefficients; these particular coefficients are tabulated in Pascal's triangle.

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