# How do you write a polynomial in standard form, then classify it by degree and number of terms 7x + 2 - 4x^2 + 8x^3?

Jun 15, 2016

standard form: $8 {x}^{3} - 4 {x}^{2} + 7 x + 2$
degree: $3$
number of terms: $4$

#### Explanation:

A polynomial in standard form is the sum/difference of terms arranged in descending degree order.

The degree of a term is the exponent of the variable of the term (if there are multiple variables in the term it is the sum of the exponents).

{: (color(black)("term"),color(white)("XXXX"),color(black)("degree")), (7x,,1), (2,,0), (-4x^2,,2), (8x^3,,3) :}

The degree of a polynomial is the degree of the term with the largest degree.

The number of terms is the number of components added/subtracted when the polynomial is expressed in standard form.

This last point is trivial in this case but note, for example,
$\textcolor{w h i t e}{\text{XXX}} \left(2 x + 3\right) \left(5 x + 1\right)$ has $\underline{3}$ terms
since when expressed in standard form:
$\textcolor{w h i t e}{\text{XXX}} \left(2 x + 3\right) \left(5 x + 1\right) = \underbrace{10 {x}^{2}} + \underbrace{17 x} + \underbrace{3}$
$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXXX")1color(white)("XXXX")2color(white)("XXX}} 3$