Monomial, PolynomialsDate: 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/ |
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