* DIVISION OF POLYNOMIALS
** OBJECTIVES
1. Divde a polynomial by a monomial
2. Divide a polynomial by a polynomial
** CONTENT
We will be  using the quotient rule, where  we subtract the
exponents if they have the same base

*** POLYNOMIAL / MONOMIAL
We Add two fractions with  a common denominator as follows,
then seperate them 

       a+b
      -----
        c

An example of this would be the following below:

      12m^6    18m^5    30m^4
     ------- + ------ + ----- = ill finish this later
       6m^2     6m^2     6m^2

The first thing  you need to do is  divide the coefficients
and  subtract  the  exponents (mentioned  in  the  quotient
rule).

                   12m^6          18m^5
                  ------ = 2m^4, ------ = 3m^3
                   6m^2           6m^2

    
*** POLYNOMIAL / POLYNOMIAL
Long  divison, you  treat the  polynomial as  if it  were a
normal number,  but you have  to follow a some  rules which
make this quite different:

         D            M           S            BD
         |            |           |             |
       Divide       Multiply    Subtract    Bring Down


These are the usual rules, but there are some additions:

1. Divide the dividend with the variable of the divisor
2. Multiply both polynomials to the answer you got from the
   first

3. Do Keep-Change-Change with the divisor after getting the
   product of the thing

4. Do it again.

**** SYNTHETIC DIVISON
Apparently technique is advanced, but is easy and can speed
things up,  There are the  things you need to  check (using
this  is  optional,  if  you aren't  required  to  do  long
division)

1. Check if the polynomials are complete, that make sure
   that the coefficients are there

2. Get the coefficients of the dividend
3. As for the variables (something like x-2), change it to
   the opposite side of it (so if its x-2, its going to
   become x + 2)

Now that you just did those things, lets use this example
of [x^2 - 5x + 6 / x-3] to do the rest of the steps.

1. Gather all the coefficients or the divident first
   
                  x^2 - 5x + 6
                   |     |   |
                   1    -5   6

2. Now do the one below:

               x + 3 | 1    -5    6
                     |
                     ---------------
                               
3. Follow BDMA (Bring Down, Multiply, add) until you get to
   the  point that  the last  term hits  zero, after  that,
   check the  term with  the highest exponent  and subtract
   said exponent by 1, then copy it to the first term