Posted by Amelie on Sunday, December 2, 2007 at 4:37pm.
First find one root by trial and error. Call it a. Then divide (x-a) into the cubic using long division to get a quadratic equation. Get the roots of that by the usual method.
For the equation
-x^3+2x^2+4x-8,
one of the roots is x=2. Divide (x-2) into -x^3+2x^2+4x-8, and you get
-x^2 + 4 = (4-2)(x+2)
That completes the factoring.
-x^3+2x^2+4x-8 = (x-2)(x+2)(2-x)
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