Solve f(x)=x^3/4-3x

$$f ( x ) = \frac { x ^ { 3 } } { 4 } - 3 x$$

Evaluate

$$\frac{x^{3}}{4}-3x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -3x times \frac{4}{4}.

$$\frac{x^{3}}{4}+\frac{4\left(-3\right)x}{4}$$

Since \frac{x^{3}}{4} and \frac{4\left(-3\right)x}{4} have the same denominator, add them by adding their numerators.

$$\frac{x^{3}+4\left(-3\right)x}{4}$$

Do the multiplications in x^{3}+4\left(-3\right)x.

$$\frac{x^{3}-12x}{4}$$

Factor

$$\frac{x\left(x^{2}-12\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{x^{3}-12x}{4}$$

Consider x^{3}-12x. Factor out x.

$$x\left(x^{2}-12\right)$$

Rewrite the complete factored expression. Polynomial x^{2}-12 is not factored since it does not have any rational roots.

$$\frac{x\left(x^{2}-12\right)}{4}$$