Solve x^3-frac{sqrt{6}}{2}x

$$x ^ { 3 } - \frac { \sqrt { 6 } } { 2 } x$$

Evaluate

$$x^{3}-\frac{\sqrt{6}x}{2}$$

Short Solution Steps

Express \frac{\sqrt{6}}{2}x as a single fraction.

$$x^{3}-\frac{\sqrt{6}x}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3} times \frac{2}{2}.

$$\frac{2x^{3}}{2}-\frac{\sqrt{6}x}{2}$$

Since \frac{2x^{3}}{2} and \frac{\sqrt{6}x}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x^{3}-\sqrt{6}x}{2}$$

Factor

$$\frac{x\left(2x^{2}-\sqrt{6}\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{2x^{3}-\sqrt{6}x}{2}$$

Consider 2x^{3}-\sqrt{6}x. Factor out x.

$$x\left(2x^{2}-\sqrt{6}\right)$$

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

$$\frac{x\left(2x^{2}-\sqrt{6}\right)}{2}$$