Question 684490
<pre>
A polynomial must be equivalent to an expression with a finite number of
terms all of which are in the form ħAx<sup>N</sup> where N is a non-negative
whole number, which includes 0, but not negative numbers.  A can be any
number, positive, negative or 0.  

f(x) = {{{(3x^2-7x)/x^3}}} is not a polynomial because it has a variable
in a denominator.  Its numerator is a polynomial and its denominator is
a polynomial, but f(x) itself is not a polynomial.

Even if it is written as

f(x) = {{{3x^2/x^3}}}{{{""-""}}}{{{7x/x^3}}}

and then as

f(x) = {{{3/x}}}{{{""-""}}}{{{-7/x^2}}} where x is not = 0, its terms are not of the form ħAx<sup>N</sup>, 
where A is any number and N a non-negative whole number.

And even if it is further written as

f(x) = {{{3x^(-1)}}}{{{""-""}}}{{{7x^(-2)}}} where x is not = 0, its terms are not of the form ħAx<sup>N</sup>, 
where A is any number and N a non-negative whole number. 
 
So f(x) cannot be changed into a finite number of terms all of the form
Ax<sup>N</sup>, where A is any number and N a non-negative whole number. 
So f(x) is not a polynomial.

Edwin</pre>