Associated Topics || Dr. Math Home || Search Dr. Math

### Factoring Fractions

```
Date: 12/7/95 at 19:12:41
From: Anonymous
Subject: dividing polynomials by monomials

12ax+16x
________   =  ?
4x

I just don't understand how to do this.
```

```
Date: 12/23/95 at 22:28:55
From: Doctor Elise
Subject: Re: dividing polynomials by monomials

Hi!

The best way to tackle this one is to try factoring the first
polynomial.

12ax + 16x

The first thing I notice, is that both expressions
have an 'x' in them, so we can pull it out like this:

x(12a + 16)

(I've grouped the expressions together and multiplied the group
by 'x', after dividing each expression by 'x').

Next, I look at 12 and 16, (especially since I already
know I have to divide by 4x) and realize they're both
divisible by 4, so I can pull the 4 out the same way, and I get:

4x(3a + 4)

Now the problem is easy, because I have 4x times something
divided by 4x, and the 4x's cancel each other out (because anything
divided by itself is 1)

so I end up with 4x(3a + 4)
__________   = 3a + 4
4x

Does this help?  Whenever you get a problem like this, the first
thing to try is to see if the part you're dividing by (the '4x', in
this case) is a factor of each expression in the numerator.

You'd do the same thing if you had (3 * 2 * 5) + (3 * 7)
___________________
3

You'd know to look for '3' as a common factor in each expression.

Extra Credit:

Can you find the answer to the problem I just posed?

- Doctor Elise,  The Geometry Forum

```
Associated Topics:
Middle School Algebra

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search