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Cubic polynomial unable to be factored nicely

  1. Mar 6, 2013 #1
    Found this on a test for an integrated algebra 2 high school math class!

    Factor completely.

    6x3 - 3x2 + 12

    3. The attempt at a solution

    3( 2x3 - x2 + 4) eq.1

    At this point I checked for rational roots using the rational roots theorem and synthetically dividing. I got nothing.

    Although this doesn't get us anywhere x2 can be factored out of the first two terms:

    3[ x2(2x-1) +4)] eq. 2

    I then plugged this guy into Wolfram and it is giving me 1 nasty irrational and 2 nasty complex roots. I'm convinced this is NOT "nicely" factorable. Does anyone have any insights?
  2. jcsd
  3. Mar 6, 2013 #2


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    Homework Helper

    You're correct that it can't be factorized using the rational root theorem, so as such, I wouldn't go any further with it. Since it was in a past exam, I'm sure it was a typo that they ended up correcting for the students on the day.
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