Michael B. answered • 11/13/12

I can provide your 'A-HA' moment

Well let's first answer the question of what is a "polynomial". The answer is a sum of terms that are composed of variables and/or constants that are multiplied together, and have non-negative exponents. A "monomial" is just one of these terms.

Thus, x^{2} + 3x + 2 is a polynomial, and is made up of three monomial terms: x^{2}, 3x, and 2. They can certainly be more complicated, such as -6x^{3}y^{5}z^{4}.

There are other similar terms: a "binomial" is a polynomial with two summed terms, a "trinomial" is a polynomial with three summed terms. Any higher, and although they do have names, we typically just call them "n^{th} order".

We typically restrict the powers on the variables to non-negative numbers, because the equation could then be simplified (in a sense) by finding a common denominator. To keep things simple, we therefore require polynomials (and their component monomials) to have positive exponents.