# How do you write a polynomial in standard form, then classify it by degree and number of terms 12x^3 + 5 - 5x^2 - 6x^2 + 3x^3 + 2 - x?

Dec 23, 2017

Combine like terms to simplify it into a polynomial.

#### Explanation:

Let's combine like terms first (i.e. Anything with ${x}^{3}$ can be combined, anything with ${x}^{2}$ can be combined, etc.):

$12 {x}^{3} + 5 - 5 {x}^{2} - 6 {x}^{2} + 3 {x}^{3} + 2 - x$
(Resort the numbers into standard form, to make it easier to simplify)
$12 {x}^{3} + 3 {x}^{3} - 5 {x}^{2} - 6 {x}^{2} - x + 5 + 2$
(Combine like terms)
$15 {x}^{3} - 11 {x}^{2} - x + 7$

We now have our simplified polynomial. This can be classified as a 3rd degree polynomial
We classify by number of terms by finding how many individual terms there are. $15 {x}^{3}$, $11 {x}^{2}$, $x$, and $7$ are all four of our terms, so we have a polynomial (Any polynomial with four or more terms is just called a polynomial.)
We classify by degree by finding the highest exponent on any of the terms. The exponent 3 is the highest term, so this polynomial is a 3rd degree polynomial.