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Dividing Polynomials by Binomials

Posted on 2005-04-17
Medium Priority
Last Modified: 2008-01-09
(You may change the numbers to the problem below)

I have a problem like:

x^2 + 7x +10   /        x + 2

I do not know what to do at all. It looks to me like it is pretty much basic long division, only
with variables?

The problem is though I was never taught long division. Any help with this would
be great, thanks.
Question by:List244
LVL 31

Accepted Solution

GwynforWeb earned 1000 total points
ID: 13802938
here is a site to start with

LVL 27

Expert Comment

ID: 13803348
In problems such as you gave the usual method is to factor the numberator. In this case one of the factors is the demonimator hence cancels and the answer comes right out.
I repeat, if this is a school problem, it belongs to a large class, the methoid of solution of which is to factor the numerator into factors, one of which is the demonminator.

Factoring is an emperical skill. That is, it is done by trial and error, enhanced by practice (and certain observations.
Note: if you change the numbers, you will almost certainly make the problem MUCH harder

If you want help on factoring, ask.

If you want help on long division of numbers, ask.

Assisted Solution

mathbiol earned 1000 total points
ID: 13803379

If you find the idea of first learning long division of numbers daunting, I think you can skip that.  I looked at GwynforWeb's helpful link.  You can skip their analogy with long division of numbers and go right to their "factor quadratics" topic at
Knowing how to factor will help you a lot with these division problems.

Here is an alternate approach.  I will try to explain how you could do your type of problem without making it look like long division.  See which approach works better for you.

Let's divide x² + 5x - 14 by (x - 2).  (This is slightly harder than your example, because yours doesn't have any negative signs.)

Think "(x - 2) times what will give me x²?"  The answer is x.  Well, x * (x - 2) is x² - 2x.  What we're aiming for is actually x² + 5x etc.  So we're 7x short of the goal.  Now think "(x - 2) times what will give me 7x?"  The answer is 7.  Well, 7 * (x - 2) is 7x - 14.  The -14 is exactly what we were shooting for.

Now we collect everything we multiplied by: x, 7.  So the answer is x + 7.

It's very important to check. Multiply (x - 2) * (x + 7) to make sure you get what you started out with.  Are you solid on this kind of multiplication?


Author Comment

ID: 13803519
This has all been helpful, however for the purpose of the class I have
to learn the long division method. I missed the classes for this chapter
and do not know what exactly he expects for the coming test. Not smart,
I know, but it's too late now. So I am stuck learning everything in the
chapter, every method there.

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