Solve 1-x^3/27

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

Evaluate

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

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{27}{27}.

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

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

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

Factor

$$\frac{\left(x-3\right)\left(-x^{2}-3x-9\right)}{27}$$

Solution Steps

Factor out \frac{1}{27}.

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

Consider 27-x^{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 -1. One such root is 3. Factor the polynomial by dividing it by x-3.

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

Rewrite the complete factored expression. Polynomial -x^{2}-3x-9 is not factored since it does not have any rational roots.

$$\frac{\left(x-3\right)\left(-x^{2}-3x-9\right)}{27}$$