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\left(a+3\right)\left(2a^{2}-a+4\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 12 and q divides the leading coefficient 2. One such root is -3. Factor the polynomial by dividing it by a+3. Polynomial 2a^{2}-a+4 is not factored since it does not have any rational roots.