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**.

__Example:__ The polynomial has 4 elements: $ \{ x^3, 3x^2, 3x, 1 \} $

$ x^3 $ a for exponent $ 3 $

$ 3x^2 $ a for exponent $ 2 $

$ 3x $ a for exponent $ 1 $

$ 1 $ a for exponent $ 0 $

The maximum power is $ 3 $, so $ P(x) $ is of degree $ 3 $ (third degree).

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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