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

May 19, 2016

Standard form: $2 {x}^{2} + x$
Number of terms: binomial

#### Explanation:

To write a polynomial in standard form, you write starting with the term with the highest degree, or exponent (in this case, the ${x}^{2}$ term), and then in decreasing order. Since the ${x}^{2}$ term is the term with the highest degree:
$2 {x}^{2} + x$

To classify a polynomial by degree, you look at the highest exponent, or degree. Since 2 is the highest exponent ($2 {x}^{2}$), it is a quadratic. Here are the first few:
Highest Exponent:
$1$- linear
$2$- quadratic
$3$- cubic
$4$- quartic
$5$- quintic

To classify a polynomial by the number of terms, count how many terms are in the polynomial: In this polynomial, there are two terms, $2 {x}^{2}$ and $x$. So, this is a binomial.

1 term- monomial
2 terms- binomial
3 terms- trinomial
4+ terms- polynomial