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3\left(3x^{3}-2x^{2}-6x-4\right)
Factor out 3.
\left(x-2\right)\left(3x^{2}+4x+2\right)
Consider 3x^{3}-2x^{2}-6x-4. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -4 and q divides the leading coefficient 3. One such root is 2. Factor the polynomial by dividing it by x-2.
3\left(x-2\right)\left(3x^{2}+4x+2\right)
Rewrite the complete factored expression. Polynomial 3x^{2}+4x+2 is not factored since it does not have any rational roots.