# How do you determine if 5n^3+nq^3 is a polynomial and if so, how do you identify if it is a monomial, binomial, or trinomial?

May 24, 2017

It is a binomial.

#### Explanation:

Let us first consider a term. A term is a product of one or more variables along with a constant, say of the type $- {p}^{2} q$ - here while $p$ is multipied twice, $q$ is multiplied once and constant term is $- 1$. Or say $x y {z}^{3}$ - here while $x$ and $z$ are multiplied once eah, $z$ is multipied thrice, and constant term is $1$.

Observe that variables are multiplied but not addedor subtracted.

Such an expression with a single term is called a monomial.

However, when two or more terms are added they are called binomial, trinomial or polynomial depending on number of terms.

An expression with two terms is called a binomial e.g. $x - {y}^{2} z$,

an expression with three terms is called a trinomial such as $- 3 {p}^{2} + 8 p q + 7 {q}^{2}$

and an expression with more than three terms is called a polynomial.

Hence, $5 {n}^{3} + 3 n {q}^{3}$ is a binomial.