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Cubic question

  1. Apr 20, 2010 #1
    I am feeling stupid over this one but I cannot remember how to solve it. I have the following cubic equation:
    4x^3 - 32x = -12

    I get the solution of x = -3 but not the other two.
    I initially had it factored as: 4x(x^2 - 8) = -12
    Did 4x = -12, got x = -3
    But then I could not get the other two solutions.

    Sorry for the simple question, just can't remember what you're supposed to do on these.
    Last edited: Apr 20, 2010
  2. jcsd
  3. Apr 20, 2010 #2


    Staff: Mentor

    This is not a useful factorization: 4x(x^2 - 8) = -12
    Write your equation as 4x^3 - 32x +12 = 0. Since x = -3 is a solution, then x + 3 must be a factor.

    This means that you have (x + 3)(?) = 0, where ? is a quadratic expression, which is easier to factor than a cubic.
  4. Apr 20, 2010 #3
    Thanks for your reply; I'm still not following where I need to go from there?
  5. Apr 20, 2010 #4


    Staff: Mentor

    Use polynomial division to divide 4x^3 - 32x +12 by x + 3.
  6. Apr 20, 2010 #5
    I happen to have a cheat sheet for the general method to solve cubic equations, so I'll post it.

    Don't take this to mean you shouldn't follow the advice given above. When you see a simple method, there is no good reason not to use it.

    You'll see that your equation is already in the normal form (EDIT: that is, if you divide your equation by 4), and the solution is easier in that case.

    Attached Files:

    Last edited: Apr 20, 2010
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