What is a polynomial?

Let's start simple. First, let's break up the word. The prefix "poly" is Greek meaning many or more than one. (Root Words, 2005). Remember what a polygon is? A many sided shape. The second half of the word in our case can mean terms. So, you can think of a polynomial as something with many terms. We can more specifically identify certain polynomials as monomials, binomials, and trinomials. You are more familiar with these prefixes than you might think. Look at the figure below.

A monomial is a single term. It can have integers, fractions, variables, and variables with positive whole exponents. A binomial combines two monomials by addition or subtraction. Similarly, a trinomial combines- you guessed it- three monomials. (See below) Warning: When looking at the terms of a monomial, make sure there are no variables in the denominator or as an exponent. Examples: 2/x, 2^x.
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What does a polynomial look like?
Review how to find the slope of a first degree polynomial by exploring the applet below.