Question

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?

Answer 1

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^2q` - here while `p` is multipied twice, `q` is multiplied once and constant term is `-1`. Or say `xyz^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^2z`,

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

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

Hence, `5n^3+3nq^3` is a binomial.