Question 1057009
Unfortunately, the direct solution formula for a cubic equation is very, very ugly.


The better way to solve something like this is to find one solution that works, and 
then use that to factor a term out of the expression, which will reduce the rest of
it to a quadratic expression. You can then either factor the quadratic, or use the 
quadratic formula.


For this problem, it is pretty easy to see that x = 1 will be a solution, since it gives:


1 - 13(1) + 12 = 0

1 - 13 + 12 = 0

-12 + 12 = 0

0 = 0


Since x = 1 is a solution, you know that (x - 1) is a factor.


Using polynomial division, divide {{{x^3 - 13x + 12}}} by (x - 1), to get:


{{{x^2 + x - 12}}}


Thus, {{{x^3 - 13x + 12 = (x - 1)(x^2 + x - 12)}}}


Next, factor {{{x^2 + x - 12}}} to get {{{(x - 3)(x + 4)}}}


This means that:


 {{{x^3 - 13x + 12 = (x - 1)(x - 3)(x + 4)}}}


And from the factors on the right hand side, you can see that 
the solutions are <strong>-4, 1, and 3</strong>.