Solve -x/22x^2+x/2

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

Evaluate

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

Short Solution Steps

Cancel out 2 and 2.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

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

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

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

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

Factor

$$\frac{x\left(1-2x^{2}\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{-2xx^{2}+x}{2}$$

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

$$x\left(-2x^{2}+1\right)$$

Rewrite the complete factored expression. Polynomial -2x^{2}+1 is not factored since it does not have any rational roots.

$$\frac{x\left(-2x^{2}+1\right)}{2}$$