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?

1 Answer
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^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.