Difference between revisions of "Coefficient"

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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. 
  
In [[mathematics]], a '''coefficient''' is a [[constant]] multiplicative [[factor]] of a specified objectThe object can be a [[variable]], a [[vector]], a [[function]], or anything else that might be subject to multiplication.
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For example, the coefficient of <math>a</math> in the [[expression]] <math>5a + b</math> is 5Note 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>.
  
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>.
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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>.
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== Leading Coefficient ==
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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.
  
Coefficients come up most frequently in a discussion of [[polynomial]]s.
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==Usage==
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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 ==
 
== See Also ==

Latest revision as of 21:38, 6 October 2020

In mathematics, a coefficient is a constant multiplicative 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 $a$ in the expression $5a + b$ is 5. Note that it is important that we specify what we are looking at the coefficients of: 5 also has a coefficient in $5a + b$, namely $a$.

Coefficients come up most frequently in a discussion of polynomials, for example, in the polynomial $\frac{5}{3}x^3 + 3x^2 + 9x + 8$, the coefficient for $x^3$ is $\frac{5}{3}$, the coefficient for $x^2$ is $3$, and the coefficient for $x$ is $9$.

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 $a$, $b$, and $c$ in the Quadratic Formula, $\frac{b\pm\sqrt{b^2-4ac}}{2a}$ are all coefficients of the polynomial $ax^2+bx+c$.

See Also