Polynomials  Long Division
A polynomial looks like this:

example of a polynomial
this one has 3 terms 
Dividing
The Method
First, write it down neatly:

 the denominator (bottom polynomial) goes first,
 then a ")",
 then the numerator (top polynomial) with a line above it.

Both polynomials should have the "highest order" terms first (those with the largest exponents, like the "2" in x^{2}).
Then:

 Divide the first term of the numerator by the first term of the denominator, and put that in the answer.
 Multiply the denominator by that answer, put that below the numerator
 Subtract to create a new polynomial


Repeat, using the new polynomial 
It is easier to show with an example!
Example:
Write it down neatly like below, then solve it stepbystep (press play):
Remainders
The previous example worked perfectly, but that is not always so! Try this one:
After dividing we were left with "2", this is the "remainder".
The remainder is what is left over after dividing.
But you still have an answer, just put the remainder divided by the denominator as part of the answer, like this:
"Missing" Terms
Sometimes there will be "missing terms" (example: there may be an x^{3}, but no x^{2}). In that case either leave gaps, or include the mssing terms with a coefficient of zero.
Example:
Write it down with "0" coefficients for the missing terms, then solve it normally (press play):
When solving it I just left gaps, and as you can see it was important to have the space available because we needed it for "3x^{3}"
More than One Variable
So far we have been dividing polynomials with only one variable (x), but how do you handle polynomials with two or more variables (such as x and y)? You can still use the same method.
Example:
