PolynomialDivision is the extension of LongDivision to polynomials or probably arbitrary fields ( http://en.wikipedia.org/wiki/Field_(mathematics) ).
Example:
(2x^2 + 3x + 1) / (x + 2) =
-(2x(x + 2)) 2x
------------
-x + 1
-(-(x + 2)) -1
-----------
3 Remainder 3
i.e. = 2x -1 + 3/(x + 2)
Helpful for simplification and when solving for roots ( http://en.wikipedia.org/wiki/Root_(mathematics) ).
I find the above layout unreadable. I prefer this:
2x - 1
+------------------------
x + 2 | 2x^2 + 3x + 1
2x^2 + 4x
-----------
-x + 1
-x - 2
----------
+ 3
So 2x^2 + 3x + 1 = (x+2)*(2x-1) + 3