[Potironette]

Can synthetic division not be used for fractional rational roots?

(I was doing a problem to solve for all real roots of p(x) = 3x³ - 5x² - 8x - 2 and I got -1/3 as a real root using rational roots theorem. Trying to find the rest of the roots by using synthetic division with -1/3 gave me a wrong answer, but long dividing the original 3x³ - 5x² - 8x - 2 by 3x + 1 worked fine.)