(x^3-8)/(x^2+2x+4) please help simplify

This problem can be done either of two ways.
You are probably supposed to do it by factoring.

     x³ - 8
 -------------
  x² + 2x + 4 

You MUST memorize the methods of factoring
the sum or difference of two cubes if you
haven't memorized them already. They are:

A³ + B³ factors as (A + B)(A² - AB + B²)
A³ - B³ factors as (A - B)(A² + AB + B²)

Yes, you MUST memorize them!

The numerator of the fraction is x³ - 8,
which can be written x³ - 2³, so it can
be factored as (x - 2)(x² + 2x + 4)

  (x - 2)(x² + 2x + 4)
 ----------------------
       x² + 2x + 4

OR

  (x - 2)(x² + 2x + 4)
 ----------------------
      (x² + 2x + 4)

Now you can cancel the (x² + 2x + 4)'s

             1
  (x - 2)(x² + 2x + 4)
 ----------------------
      (x² + 2x + 4)
          1

and all that's left is

    (x - 2)

or

     x - 2
 
=====================

The other way to do that problem is by long division.
But your teacher probably wanted you to do it by
factoring instead. But here is how it could have
been done by long division:


     x³ - 8
 -------------
  x² + 2x + 4


                        x - 2
x² + 2x + 4)x³ + 0x² + 0x - 8
            x³ + 2x² + 4x
                -2x² - 4x - 8
                -2x² - 4x - 8
                            0   

Edwin