Examples:

1)Given x3 - 2x2 - 5x + 6 with one factor being (x + 2), find the 
remaining factors.

SOLUTION:
If (x + 2) is a factor, then (x + 2) must divide x3 - 2x2 - 5x + 6 exactly 
(i.e. there are no remainders!!)

Set up the problem using long division: 
                                                          -----
           ------------------            (note that this |      sign is the
   (x + 2)| x3 - 2x2 - 5x + 6              one often used for long division)

STEP 1:
Look at only the first term, x, in the given factor (x + 2) and see what value,
when multiplied by this term will give you the first term in the expression 
being divided.  In this case, the value would be x2 because x2(x) = x3.
Put this value in top of the line just like in regular division. It now looks
like this: 
            x2
           -------------------
   (x + 2)| x3 - 2x2 - 5x + 6 

STEP 2: 
Multiply this value that is now on top by the whole factor you are dividing 
by and write it below the expression being divided 
(i.e. x2(x + 2) = x3 + 2x2 )  Thus:


            x2
           -------------------
   (x + 2)| x3 - 2x2 - 5x + 6 
            x3 + 2x2
            

STEP 3: 
Subtract this new expression from hte original expression and write the answer 
on the next line.  Bring down the next term from the original expression and 
write it next to your answer.  It should look like:


            x2
           -------------------
   (x + 2)| x3 - 2x2 - 5x + 6 
            x3 + 2x2
            ---------
                -4x2 - 5x

STEP 4: 
Repeat Steps 1-3 again with the expression of interest now being (-4x2 - 5x).
It should end up looking like this:


            x2 - 4x + 3
           -------------------
   (x + 2)| x3 - 2x2 - 5x + 6 
            x3 + 2x2
            ---------
                -4x2 - 5x
                -4x2 - 8x
                ---------
                       3x + 6
                       3x + 6
                       ------
                          0  

So the other factor of x3 - 2x2 - 5x + 6 besides (x + 2)
is (x2 - 4x + 3).  But this factor can be factored further into
(x - 1) and (x - 3) (by decomposition).  Thus,
x3 - 2x2 - 5x + 6 = (x + 2)(x - 1)(x - 3)



2) Given ( x - 2) as a factor, find the other factor of 
   x3 - 2x2 + 3x - 6.

SOLUTION:
              x2 + 0x + 3
             ------------------
     (x - 2)| x3 - 2x2 + 3x - 6
              x3 - 2x2
              --------
                   0x2 + 3x 
                   0x2 - 0x
                   ---------
                         3x - 6
                         3x - 6
                         ------
                            0

The other factor is then (x2 + 3) [omit the 0x term].   
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