Monomial, Polynomials

Date: 11/14/97 at 16:42:50
From: Ron Gumbosky
Subject: I have a question

Dear Dr. Math,

My name is April Marie and I am having trouble with my pre-algebra
homework. I need to know what a monomial is. I looked it up in your
dictionary of math terms but I didn't understand it. Can you please
explain it to me in simple terms?

April Marie

Date: 11/23/97 at 18:30:19
From: Doctor Bill
Subject: Re: I have a question

Dear April Marie,

A monomial is a polynomial with only one term. What, then, is a 
polynomial?  

A polynomial is an algebraic expression with terms consisting of 
coefficients and variables, raised only to non-negative integer 
powers. If that explanation makes sense to you, then you are set... 
But perhaps you should see some examples.

2x^5 + 9x^4 - 7x^3 + 3x^2 - 5x +1  is a polynomial with 6 terms. 
Can you see the 6 terms? Each has a number in front and then the 
variable x raised to a power which is a non-negative integer.  This
is clearer if we write it as

  2x^5 + 9x^4 - 7x^3 + 3x^2 - 5x^1 + 1x^0

and note that x^0 is equal to 1. 

There is no special name for a polynomial with 6 terms. There are 
special names for some polynomials, though.

4x^2 + x + 5 is a polynomial called a TRINOMIAL because it has 3 
terms. (Do you see where the name came from, and does it make sense to 
you?) Notice that the middle term, x, seems to have no coefficient, 
but it does. The coefficient of the middle term is 1. Whenever you 
don't "see" a coefficient, it is 1 .

3x - 5 is a polynomial called a BINOMIAL because it has 2 terms. (Does 
this name also seem to make sense?)

Now, what do you suppose a monomial would look like, and what 
definition could you make up to define it?

-Doctor Bill,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/