Let's try this: Assume that one root of the polynomial is c. Use this c as divisor in sythetic division:
______________________________________ c / 6 0 2 -8 -c 6c 6c^2 6c^3+2c 6c^4+2c^2-8c ----------------------------------------------------------------- 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.
