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Polynomial Degree

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

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Polynomial Degree -

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# 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 $x = x^1$

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