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Factorising cubic

  1. Jan 23, 2016 #1
    1. The problem statement, all variables and given/known data
    The curve C with equation y = f(x) passes through the point (5, 65).
    Given that f'(x) = 6x2 -10x - 12,
    a) use integration to find f(x)
    b) Hence show that f(x) = x(2x+3)(x-4)

    3. The attempt at a solution
    I have no problem with this question, except it seems the given function for b) might be wrong or at least not complete.
    a) integrated for y = 2x3 - 5x2 - 12x + c
    65 = 2(5)3 - 5(5)2 - 12(5) + c
    = 200 - 125 - 60 + c = 15 + c.
    65 - 15 = 50 = c,
    Therefore y = 2x3 - 5x2 - 12x + 50.
    b) Taking out x, we get x(2x2 - 5x - 12) + 50.
    This factors into x(2x+3)(x-4) + 50. So the given function is missing the +50. My fault or printing error?
     
  2. jcsd
  3. Jan 23, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    2*53 is not 200.
     
  4. Jan 23, 2016 #3
    Argh... thanks. I went over that 4 or 5 times and didn't catch it out.
     
  5. Jan 23, 2016 #4

    SteamKing

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    Staff Emeritus
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    Homework Helper

    For future reference, a solitary factor of x implies that the constant term is zero in the full polynomial.
     
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