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