Tool to find the degree (or order) of a polynomial, that is, the greatest power of the polynomial's variable.

Polynomial Degree - dCode

Tag(s) : Functions

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The degree of a polynomial is the greatest power (exponent) associated with the polynomial variable. The degree is also called the order of the polynomial.

__Example:__ The trinomial $ x^2 + x + 1 $ of variable $ x $ has for greatest exponent $ x^2 $ that is $ 2 $, therefore the polynomial is of degree $ 2 $ (or the polynomial is of the second degree, where the polynomial is of order $ 2 $)

The degree is sometimes noted $ \deg $

To find the degree of a polynomial, it is necessary to have the polynomial written in expanded form.

__Example:__ $ P(x) = (x+1)^3 $ expands $ x^3 + 3x^2 + 3x + 1 $

Browse all the elements of the polynomial in order to find the maximum exponent associated with the variable, this maximum is the degree of the polynomial.

The degree of a polynomial having a variable degree remains the maximum value of the exponents of the elements of the polynomial.

__Example:__ $ x^n+x^2+1 $ has for degree $ \max (n,2) $, which therefore depends on the value of $ n $, the degree will be $ n $ if $ n > 2 $ otherwise $ 2 $.

The degree of a polynomial is dependent on the associated variable. If there are several variables, calculate the degree of the polynomial for each variable.

The polynomial $ x $ (also called monomial) has for degree $ 1 $ because $ x = x^1 $

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*Polynomial Degree* on dCode.fr [online website], retrieved on 2023-10-01,

degree,polynomial,order,1st,first,2nd,second,3rd,third

https://www.dcode.fr/polynomial-degree

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