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Why does polynomial long division work?

  1. Feb 5, 2013 #1
    So I'm in a college algebra class and I know how to do polynomial long division. I'm curious as to why polynomial long division works. I've looked at some proofs, but they use scary symbols that I don't understand (I am quite dumb). Do I need very high-level math to comprehend why polynomial long division works? What I'd like to see, if it's possible, is an example of a polynomial division problem being solved with just basic algebra. How would I solve, for example, (x2-x-6)/(x-1) without long division? (sorry, don't know how to use Latex)
  2. jcsd
  3. Feb 5, 2013 #2


    Staff: Mentor

    polynomial division is very similar to numerical long division.

    A common form of polynomial long division is synthetic division:


    which may show you how similar they are and why they work.
  4. Feb 5, 2013 #3


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    Staff Emeritus
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    Have you tried factoring the numerator?
    Last edited by a moderator: Feb 5, 2013
  5. Feb 5, 2013 #4


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    Since neither factor is x- 1, I don't believe factoring helps with the division.

    Instead write this as
    [tex]\frac{x^2- x}{x- 1}+ \frac{-6}{x- 1}= \frac{x(x- 1)}{x- 1}+ \frac{-6}{x- 1}[/tex]
    [tex]= x+ \frac{-6}{x- 1}[/tex]
    so x- 1 divides into [itex]x^2- 1[/itex] x times with remainder -6.

    You could also use "synthetic division" as shown here: http://www.purplemath.com/modules/synthdiv.htm
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