Solve F(t)=1/4t^4-1/2t^2

$$F ( t ) = \frac { 1 } { 4 } t ^ { 4 } - \frac { 1 } { 2 } t ^ { 2 }$$

Factor

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

Solution Steps

Factor out \frac{1}{4}.

$$\frac{t^{4}-2t^{2}}{4}$$

Consider t^{4}-2t^{2}. Factor out t^{2}.

$$t^{2}\left(t^{2}-2\right)$$

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

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

Evaluate

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