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Division of Polynomials


Date: 10 Aug 1995 02:42:13 -0400
From: Greg Sharpe
Subject: Division of Polynomials

Hi!

Would it be possible for you to send me some examples of polynomial
divisions (e.g. x^2 + x + 1 / x + 1)?  I used to be able to do it, but have
since forgotton.

Thanks,

Greg.


Date: 14 Aug 1995 20:38:19 -0400
From: Dr. Ken
Subject: Re: Division of Polynomials

Hello there!

Here's what you would do in your example problem.  As you go through this,
try to remember that all the steps are exactly the same as doing long
division with actual numbers, it's just that you have to be a little more
careful!

    _______________
x+1 ) x^2 + x + 1          What do I have to multiply x by to get x^2?  x.
                               
    ________x______
x+1 ) x^2 + x + 1     Now multiply the thing on top by the thing on the left:

    ________x______
x+1 ) x^2 + x + 1     Subtract from the row above and bring down:
      x^2 + x

    ________x______
x+1 ) x^2 + x + 1     
      x^2 + x         We can stop now, because the degree of the remainder is
      -------         less than the degree of the dividend (x-1).
            0 + 1

So the answer is x, with a remainder of 1.

Do you think you could try?  Give it a shot, and if you're having
difficulty, let us know and we'll give you another example.  

-K
    
Associated Topics:
High School Basic Algebra

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