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\left(3x-1\right)\left(x^{2}-2x-2\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 2 and q divides the leading coefficient 3. One such root is \frac{1}{3}. Factor the polynomial by dividing it by 3x-1. Polynomial x^{2}-2x-2 is not factored since it does not have any rational roots.