Solve f(x)=x^4/7-2x

$$f ( x ) = \frac { x ^ { 4 } } { 7 } - 2 x$$

Evaluate

$$\frac{x^{4}}{7}-2x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -2x times \frac{7}{7}.

$$\frac{x^{4}}{7}+\frac{7\left(-2\right)x}{7}$$

Since \frac{x^{4}}{7} and \frac{7\left(-2\right)x}{7} have the same denominator, add them by adding their numerators.

$$\frac{x^{4}+7\left(-2\right)x}{7}$$

Do the multiplications in x^{4}+7\left(-2\right)x.

$$\frac{x^{4}-14x}{7}$$

Factor

$$\frac{x\left(x^{3}-14\right)}{7}$$

Solution Steps

Factor out \frac{1}{7}.

$$\frac{x^{4}-14x}{7}$$

Consider x^{4}-14x. Factor out x.

$$x\left(x^{3}-14\right)$$

Rewrite the complete factored expression. Polynomial x^{3}-14 is not factored since it does not have any rational roots.

$$\frac{x\left(x^{3}-14\right)}{7}$$