3x^3-6x+4x^2-8=0; 3x(x^2-2)+4(x^2-2)=0=(3x+4)(x^2-2); (3x+4)(x-sqrt(2))(x+sqrt(2)).
Roots are x=-4/3, sqrt(2), -sqrt(2).
To use synthetic division, identify -4/3 as one root:
-4/3 | 1..4/3 -2 -8/3
.........1 -4/3..0..8/3
.........1.....0 -2 | 0
x^2-2 is the other factor which factorises as above.
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