Let's try this: Assume that one root of the polynomial is c. Use this c as divisor in sythetic division:
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c / 6 0 2 -8 -c
6c 6c^2 6c^3+2c 6c^4+2c^2-8c
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6 6c 6c^2+2 6c^3+2c-8 6c^4+2c^2-9c Set 6c^4+2c^2-9c=0
(remainder is zero)
and solve for c: c=0
is a solution.
In other words, if c=0, the remainder obtained thru synth. div. will be zero.
