10.1 Add and subtract polynomials

Identify polynomials, monomials, binomials, and trinomials

In Evaluate, Simplify, and Translate Expressions , you learned that a term    is a constant or the product of a constant and one or more variables. When it is of the form $a{x}^m,$ where $a$ is a constant and $m$ is a whole number, it is called a monomial. A monomial, or a sum and/or difference of monomials, is called a polynomial.

Notice the roots:

• poly - means many
• mono - means one
• bi - means two
• tri - means three

Here are some examples of polynomials:

Notice that every monomial, binomial, and trinomial is also a polynomial. They are special members of the family of polynomials and so they have special names. We use the words ‘monomial’, ‘binomial’, and ‘trinomial’ when referring to these special polynomials and just call all the rest ‘polynomials’.

Determine the degree of polynomials

In this section, we will work with polynomials that have only one variable in each term. The degree of a polynomial and the degree of its terms are determined by the exponents of the variable.

A monomial that has no variable, just a constant, is a special case. The degree of a constant is $0$ —it has no variable.

Let's see how this works by looking at several polynomials. We'll take it step by step, starting with monomials, and then progressing to polynomials with more terms.

Remember: Any base written without an exponent has an implied exponent of $1.$