Solve quadg(x)=1/2x^3-1/2x

$$\quad g ( x ) = \frac { 1 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } x$$

Factor

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

Solution Steps

Factor out \frac{1}{2}.

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

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

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

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)$$

Rewrite the complete factored expression.

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

Evaluate

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