Factoring to Find the Limit

Date: 11/5/95 at 23:2:15
From: John Florance
Subject: limits...

Hi Doc...
             3
lim         x   +   8
x -> -2    -----------      =       ???
            x   +   2

i.e., how to factor the numerator?

John

Date: 11/6/95 at 11:7:0
From: Doctor Ethan
Subject: Re: limits...

Hey John,

Here is the deal.

We have to factor the top into two factors so that we can cancel with 
the bottom.  Fortunately there is a standard rule for factoring things
that are in the form of a^3 + b^3

If I tell you the first factor do you think you can figure out the 
second?

The first looks like a + b  or in the case of this problem x + 2.  
So what would the second factor have to be in order to work out?

I will tell you that it is a trinomial of highest power two.

So you need to figure out: 

(x + 2)(what goes here) = (x^3 + 8)

Have fun.  I think that you can figure it out.

If you can't, write back and we will help you.

-Doctor Ethan,  The Geometry Forum