SOLUTION: (b) Solve for x, the equation 12x3 + 8x2 - x - 1 = 0. (All solutions are rational and between �1.)

Question 330385: (b) Solve for x, the equation 12x3 + 8x2 - x - 1 = 0. (All solutions are rational and between �1.)
Answer by galactus(183) (Show Source): You can put this solution on YOUR website!

Let's try breaking it up, grouping and factoring. One could use the Rational Root Theorem as well.
Rewrite:

Group:

Factor out 3x from the first 3 terms and -1 from the last 3 terms:

What makes 3x-1=0?. x=1/3
What makes 2x+1=0?. x=-1/2
Since x=-1/2 has multiplicity 2, we have three roots as required of the cubic.

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