Solve -x^3/8-x^2/4-x/2=

$$- \frac { x ^ { 3 } } { 8 } - \frac { x ^ { 2 } } { 4 } - \frac { x } { 2 } =$$

Evaluate

$$-\frac{x\left(x^{2}+2x+4\right)}{8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 4 is 8. Multiply \frac{x^{2}}{4} times \frac{2}{2}.

$$-\frac{x^{3}}{8}-\frac{2x^{2}}{8}-\frac{x}{2}$$

Since -\frac{x^{3}}{8} and \frac{2x^{2}}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-x^{3}-2x^{2}}{8}-\frac{x}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 2 is 8. Multiply \frac{x}{2} times \frac{4}{4}.

$$\frac{-x^{3}-2x^{2}}{8}-\frac{4x}{8}$$

Since \frac{-x^{3}-2x^{2}}{8} and \frac{4x}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-x^{3}-2x^{2}-4x}{8}$$

Factor

$$-\frac{x\left(x^{2}+2x+4\right)}{8}$$

Solution Steps

Factor out \frac{1}{8}.

$$\frac{-x^{3}-2x^{2}-4x}{8}$$

Consider -x^{3}-2x^{2}-4x. Factor out x.

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

Rewrite the complete factored expression. Polynomial -x^{2}-2x-4 is not factored since it does not have any rational roots.

$$\frac{x\left(-x^{2}-2x-4\right)}{8}$$