Solve -x^2/2+x^4/24-x^4/8

$$- \frac{ { x }^{ 2 } }{ 2 } + \frac{ { x }^{ 4 } }{ 24 } - \frac{ { x }^{ 4 } }{ 8 }$$

Factor

$$\frac{x^{2}\left(-x^{2}-6\right)}{12}$$

Solution Steps

Factor out \frac{1}{24}.

$$\frac{-12x^{2}+x^{4}-3x^{4}}{24}$$

Consider -12x^{2}+x^{4}-3x^{4}. Factor out x^{2}.

$$x^{2}\left(-12+x^{2}-3x^{2}\right)$$

Consider -12+x^{2}-3x^{2}. Multiply and combine like terms.

$$-2x^{2}-12$$

Consider -2x^{2}-12. Factor out 2.

$$2\left(-x^{2}-6\right)$$

Rewrite the complete factored expression.

$$\frac{x^{2}\left(-x^{2}-6\right)}{12}$$

Simplify. Polynomial -x^{2}-6 is not factored since it does not have any rational roots.

$$\frac{\left(-x^{2}-6\right)x^{2}}{12}$$

Evaluate

$$-\frac{x^{4}}{12}-\frac{x^{2}}{2}$$