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

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].
```