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 [[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>. | 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. | + | 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 == | ||
| + | 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. | ||
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| + | ==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 == | == 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 
in the expression 
is 5. Note that it is important that we specify what we are looking at the coefficients of: 5 also has a coefficient in , namely .
Coefficients come up most frequently in a discussion of polynomials, for example, in the polynomial 
, the coefficient for 
is 
, the coefficient for 
is 
, and the coefficient for 
is 
.
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 , 
, and 
in the Quadratic Formula, 
are all coefficients of the polynomial 
.
