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Before you get started, take this readiness quiz.
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 where is a constant and is a whole number, it is called a monomial. A monomial, or a sum and/or difference of monomials, is called a polynomial.
polynomial —A monomial, or two or more monomials, combined by addition or subtraction
monomial —A polynomial with exactly one term
binomial — A polynomial with exactly two terms
trinomial —A polynomial with exactly three terms
Notice the roots:
Here are some examples of polynomials:
| Polynomial | |||
| Monomial | |||
| Binomial | |||
| Trinomial |
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 whether each polynomial is a monomial, binomial, trinomial, or other polynomial:
| Polynomial | Number of terms | Type | |
|---|---|---|---|
| ⓐ | 3 | Trinomial | |
| ⓑ | 1 | Monomial | |
| ⓒ | 5 | Polynomial | |
| ⓓ | 2 | Binomial | |
| ⓔ | 1 | Monomial |
Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial.
Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial.
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 —it has no variable.
The degree of a term is the exponent of its variable.
The degree of a constant is
The degree of a polynomial is the highest degree of all its terms.
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
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