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\left(2v-3\right)\left(-4v^{2}-6v-9\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 27 and q divides the leading coefficient -8. One such root is \frac{3}{2}. Factor the polynomial by dividing it by 2v-3. Polynomial -4v^{2}-6v-9 is not factored since it does not have any rational roots.