1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook