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Synthetic division or Long division of polynomials?

  1. Jul 20, 2007 #1
    How do i know under which circumstances to use synthetic and when to just do regular polynomial division? do they not both give the same results?
  2. jcsd
  3. Jul 20, 2007 #2

    Gib Z

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    Yes, they give the same results. They are just 2 different methods for the same thing, I prefer the long division though.
  4. Jul 20, 2007 #3
    Synthetic division only works if you are dividing a polynomial by a linear factor..
  5. Jul 20, 2007 #4


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    In fact, only when dividing by something of the form x-a.

    Synthetic division is just a simplified way of writing a division of that very special (but very important) form.
  6. Jul 24, 2007 #5


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    There is a generalization to arbitrary polynomials
  7. Jul 24, 2007 #6


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    http://www.pims.math.ca/pi/issue7/page13-16.pdf [Broken]
    Last edited by a moderator: May 3, 2017
  8. Jun 18, 2008 #7
    Hi i find them to go together, hand in hand.

    for instance, we have this problem: 8x^6 + 7x^3 -1

    i use synthetic division to find that -1 is a solution, hence i have a factor that is:

    now, to look for the rest of the factors, i use long division to divide (8x^6 + 7x^3 -1)
    by (x-1);

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