What is a monomial?

Question

What is it used for? Why was it brought up and what do i need to know about it?

Answer 1

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, x² + 3x + 2 is a polynomial, and is made up of three monomial terms: x², 3x, and 2.  They can certainly be more complicated, such as -6x³y⁵z⁴.

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.

Answer 2

http://www.mathsisfun.com/definitions/monomial.html