Solve 1/8-x^3/27=

$$\frac { 1 } { 8 } - \frac { x ^ { 3 } } { 27 } =$$

Evaluate

$$-\frac{x^{3}}{27}+\frac{1}{8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 27 is 216. Multiply \frac{1}{8} times \frac{27}{27}. Multiply \frac{x^{3}}{27} times \frac{8}{8}.

$$\frac{27}{216}-\frac{8x^{3}}{216}$$

Since \frac{27}{216} and \frac{8x^{3}}{216} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-8x^{3}}{216}$$

Factor

$$\frac{\left(2x-3\right)\left(-4x^{2}-6x-9\right)}{216}$$

Solution Steps

Factor out \frac{1}{216}.

$$\frac{27-8x^{3}}{216}$$

Consider 27-8x^{3}. 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 2x-3.

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

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

$$\frac{\left(2x-3\right)\left(-4x^{2}-6x-9\right)}{216}$$