Tool to find the degree of a polynomial

Polynomial Degree - dCode

Tag(s) : Functions

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

Tool to find the degree of a polynomial

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.

dCode retains ownership of the online 'Polynomial Degree' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Polynomial Degree download for offline use on PC, tablet, iPhone or Android !

Please, check our community Discord for help requests!

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

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

© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲