[Coda]

Okay, so brushing up on the technique...

-1/3	|	3	-5	-8	-2
.	|	_	-1	_2	_2
.	.	3	-6	-6	0

3x² - 6x - 6? Seems right to me. You must have made a mistake in your arithmetic somewhere.

EDIT: Equivalently, x² - 2x - 2, because we're finding roots; 0 * anything = 0 so we can multiply the whole thing by 1/3 and get the same results.

EDIT 2: Which... um... I usually go for the quadratic formula here:

(-(-2) +/- sqrt((-2)² - 4*1*-2)) / (2*1)
(2 +/- sqrt(4 + 8)) / 2
(2 +/- 2sqrt(3)) / 2
1 +/- sqrt(3)

The remaining two roots are irrational -- (x - 1 - sqrt(3)) and (x - 1 + sqrt(3)). You CAN, theoretically, do synthetic division on one of those to get the other, but you'd be juggling those silly radicals through the whole thing and it's probably not worth the effort.