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Factoring a polynomial where factor theorem doesn't work

  1. May 18, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve: x^3 - 9x^2 + 15x + 30

    2. Relevant equations



    3. The attempt at a solution

    The factors of 30 are +-1, +-2, +-3, +-5, +-6, +-10, +-15, and +-30.

    I used my graphing calculator and got a zero close to -1. I plugged it into the original equation and got 5, not 0. I used the zero function on my calculator and found that the zero occurred around -1.13. that's a fraction.

    How would I solve this algebraically?
     
  2. jcsd
  3. May 19, 2010 #2
    Try newtons method:
    Define
    [tex] T(x)=x-\frac{f(x)}{f'x}=x-\frac{x^3-9x^2+15x+30}{3x^2+18x+15} [/tex]
     
  4. May 19, 2010 #3

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    If you are only looking for a numerical approximation, then Newton's method should work fine for you. However, if you are looking for an exact analytical solution, try the cubic formula
     
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