Classify Monomials, Binomials, and Trinomials

Classifying by number of terms

A polynomial expression is classified by how many separate terms it has. Terms are parts of the expression separated by + or − signs. First, make sure the expression is in simplified form so that like terms are combined. Then count the terms.

How to classify

1. Simplify first if possible.
   • Combine like terms before deciding on the name.
2. Count the terms.
   • 1 term → monomial
   • 2 terms → binomial
   • 3 terms → trinomial
3. If there are more than 3 terms, it is still a polynomial, but not one of these three special names.

Important detail

A negative sign belongs to the term after it. For example, in (x^2 - 3x + 1), the terms are (x^2), (-3x), and (1), so there are 3 terms.

Check your answer

After classifying, reread the simplified expression and count again. If two terms can be combined, the original count may change. Always classify the final simplified expression, not the unsimplified one.