Last time, we did math operations using scientific notation. Let’s take a short review.

You are given an expression to evaluate using scientific notation.

Enter values for the missing terms into the text boxes. Then click the “Submit” button.

Now, let’s move on with today’s lesson.

Here we have two monomial terms, <EQUATION> and <EQUATION>.

Suppose we add them together. The result has two terms: <EQUATION> . It is not the monomial.

An expression with two monomial terms is a binomial.

Now, suppose we add another monomial term. The expression has three terms: <EQUATION>

An expression with three monomial terms is called a trinomial.

A more general name for all of these expressions is polynomial.

A polynomial is an expression that is a monomial, or a sum of monomials.

A polynomial can have any number of monomial terms.

Here we have three expressions. Which one is not a polynomial? Click the “Submit” button after selecting your answer.

If any term in an expression is not a monomial, then the expression is not a polynomial. Each of the examples here contains a quotient term which is not a monomial. Therefore, none of them are polynomials.

Monomials and polynomials are described by their degree.

The degree of a monomial is given by the sum of the exponents of its variables.

Here we have the monomial: <EQUATION>

The exponent of x is 2, and the exponent of y is 1.

Therefore, the degree of this monomial is 3.

Now, look at this polynomial: <EQUATION>

The degree of the first monomial term is 4.

The degree of the second monomial term is 1.

The third monomial term is just a number. We say its degree is 0.

What do you think is the degree of this polynomial? Click the “Submit” button after entering your answer.

The degree of a polynomial is given by the greatest degree of any of its terms.

The first term of this polynomial has the greatest degree.

Therefore, the degree of this polynomial is 4.

Now, let’s see if you can determine the degree of some polynomials.

You are given a polynomial.

Enter its degree into the text box. Then click the “Submit” button to see the answer.

We usually arrange the terms of a polynomial in a certain order. The polynomial <EQUATION> is arranged so that the powers of the <EQUATION> variable are in descending order.

The terms in the polynomial <EQUATION> are arranged so that the <EQUATION> powers are in ascending order.

In the next few lessons, we will see that this is helpful when performing operations with polynomials.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education