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### 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.

-Doctor Ethan,  The Geometry Forum

```
Associated Topics:
High School Basic Algebra

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