# How do you write a polynomial in standard form, then classify it by degree and number of terms 2x^2 + 3x^3 + 4x^4 + 5x^5?

Sep 8, 2017

standard form: $5 {x}^{5} + 4 {x}^{4} + 3 {x}^{3} + 2 {x}^{2}$
degree: 5
number of terms: 4

#### Explanation:

A polynomial in standard form has the order of it's terms in decreasing degree, where the degree of a term is the (sum of) the exponent(s) of its variables.

For example:
$\textcolor{w h i t e}{\text{XXX}} 23 {p}^{8}$ has degree $8$
and
$\textcolor{w h i t e}{\text{XXX}} 7 {r}^{2} {t}^{3}$ has degree $2 + 3 = 5$

In this case, we have the terms:
$\textcolor{w h i t e}{\text{XXX}} 2 {x}^{2}$ has degree $2$
$\textcolor{w h i t e}{\text{XXX}} 3 {x}^{3}$ has degree $3$
$\textcolor{w h i t e}{\text{XXX}} 4 {x}^{4}$ has degree $4$
$\textcolor{w h i t e}{\text{XXX}} 5 {x}^{5}$ has degree $5$
placing them in descending order requires that $5 {x}^{5}$ be the first term and $2 {x}^{2}$ be the last term (with the other 2 terms in the obvious sequence).

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The degree of a polynomial (as opposed to the degree of a single term) is the largest value of any of its terms' degrees.

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A term is an element of a polynomial separated from other elements by either addition or subtraction.