View source for Coefficient

In [[mathematics]], a '''coefficient''' is a [[constant]] multiplicative [[divisor | factor]] of a specified object.  The object can be a [[variable]], a [[vector]], a [[function]], or anything else that might be subject to multiplication.  

For example, the coefficient of <math>a</math> in the [[expression]] <math>5a + b</math> is 5.  Note that it is important that we specify what we are looking at the coefficients of: 5 also has a coefficient in <math>5a + b</math>, namely <math>a</math>.

Coefficients come up most frequently in a discussion of [[polynomial]]s, for example, in the [[polynomial]] <math>\frac{5}{3}x^3 + 3x^2 + 9x + 8</math>,  the coefficient for <math>x^3</math> is <math>\frac{5}{3}</math>, the coefficient for <math>x^2</math> is <math>3</math>, and the coefficient for <math>x</math> is <math>9</math>.

== Leading Coefficient == 
The leading coefficient is the coefficient of the highest degree in a polynomial. It is used to write the polynomial in standard form, and is especially used to factor quadratics.

==Usage==
Coefficient are often used to more easily refer to parts of a [[expression]] or a [[polynomial]]. For example, the <math>a</math>, <math>b</math>, and <math>c</math> in the [[Quadratic Formula]], <math>\frac{b\pm\sqrt{b^2-4ac}}{2a}</math> are all coefficients of the polynomial <math>ax^2+bx+c</math>. 

== See Also ==
* [[Linear algebra]]
* [[Binomial coefficient]]s
* [[Binomial theorem]]

{{stub}}
[[Category:Definition]]