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Factoring a difficult polynomial so that I can extend equation

  1. Sep 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Give a formula for the extended function that is continuous at the indicated point.

    (x3-4x2-11x+30)/(x2-4), x=2


    2. Relevant equations



    3. The attempt at a solution
    I know that I have to factor the top and bottom so that I can cancel terms that cause the function to be undefined at x=2, and I know how to do everything after that. However, I'm stuck on how to factor x3-4x2-11x+30. I know that the factors are (x-5)(x-2)(x+3), but I don't know how to go about getting there. I tried grouping, but it didn't work since there is no way that I see to factor -11x+30.
    x3-4x2-11x+30

    x2(x-4)-11x+30

    I tried grouping other ways, but they did not work either.
     
  2. jcsd
  3. Sep 7, 2011 #2

    Dick

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    Science Advisor
    Homework Helper

    In general, what you want is the rational roots theorem. If (x-r) is a factor of the numerator then r must divide 30. That gives a limited number of guesses for possible factors. But in this particular case, it's a pretty good guess that (x-2) is factor. Once you know that, divide the numerator by (x-2) to get a quadratic. Then factor the quadratic to get the other two factors.
     
  4. Sep 7, 2011 #3
    Oh gee, I completely forgot about that. (It's been a while since Algebra II) That makes total sense. Thank you so much for your help!
     
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