Solve f(x)=x^3/3-2x=

$$f ( x ) = \frac { x ^ { 3 } } { 3 } - 2 x =$$

Evaluate

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

Short Solution Steps

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

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

Since \frac{x^{3}}{3} and \frac{3\left(-2\right)x}{3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x^{3}+3\left(-2\right)x.

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

Factor

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

Solution Steps

Factor out \frac{1}{3}.

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

Consider x^{3}-6x. Factor out x.

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

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

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