Solve -1-27/8a^3

$$- 1 - \frac { 27 } { 8 } a ^ { 3 }$$

Factor

$$\frac{\left(3a+2\right)\left(-9a^{2}+6a-4\right)}{8}$$

Solution Steps

Factor out \frac{1}{8}.

$$\frac{-8-27a^{3}}{8}$$

Consider -8-27a^{3}. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -8 and q divides the leading coefficient -27. One such root is -\frac{2}{3}. Factor the polynomial by dividing it by 3a+2.

$$\left(3a+2\right)\left(-9a^{2}+6a-4\right)$$

Rewrite the complete factored expression. Polynomial -9a^{2}+6a-4 is not factored since it does not have any rational roots.

$$\frac{\left(3a+2\right)\left(-9a^{2}+6a-4\right)}{8}$$

Evaluate

$$-\frac{27a^{3}}{8}-1$$