Solve =x^3/2+3x/2

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

Factor

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

Solution Steps

Factor out \frac{1}{2}.

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

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

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

Rewrite the complete factored expression. Polynomial x^{2}+3 is not factored since it does not have any rational roots.

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

Evaluate

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

Solution Steps

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

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