Factor
\frac{\left(2x-1\right)\left(3x^{2}+2x+2\right)}{2}
Evaluate
3x^{3}+\frac{x^{2}}{2}+x-1
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\frac{6x^{3}+2x+x^{2}-2}{2}
Factor out \frac{1}{2}.
\left(2x-1\right)\left(3x^{2}+2x+2\right)
Consider 6x^{3}+2x+x^{2}-2. 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 6. One such root is \frac{1}{2}. Factor the polynomial by dividing it by 2x-1.
\frac{\left(2x-1\right)\left(3x^{2}+2x+2\right)}{2}
Rewrite the complete factored expression. Polynomial 3x^{2}+2x+2 is not factored since it does not have any rational roots.
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