Search for a tool
Polynomial Degree

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

Results

Polynomial Degree -

Tag(s) : Functions

Share
dCode and more

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!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Feedback and suggestions are welcome so that dCode offers the best 'Polynomial Degree' tool for free! Thank you!

# Polynomial Degree

## Degree of a Polynomial Finder

### What is the degree of a polynomial? (Definition)

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 $\deg$

### How to calculate the degree of a polynomial?

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).

### How to calculate the degree of a polynomial with a variable 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 $2$.

### How to calculate the degree of a multivariable polynomial?

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.

### What is the degree of the polynomial x

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

## Source code

dCode retains ownership of the "Polynomial Degree" source code. Except explicit open source licence (indicated Creative Commons / free), the "Polynomial Degree" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Polynomial Degree" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Polynomial Degree" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

## Cite dCode

The copy-paste of the page "Polynomial Degree" or any of its results, is allowed (even for commercial purposes) as long as you cite dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Polynomial Degree on dCode.fr [online website], retrieved on 2023-10-01, https://www.dcode.fr/polynomial-degree

## Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!