Solve 4s^4-4s^3+5s^2-5s

$$4 s ^ { 4 } - 4 s ^ { 3 } + 5 s ^ { 2 } - 5 s$$

Factor

$$s\left(s-1\right)\left(4s^{2}+5\right)$$

Solution Steps

Factor out s.

$$s\left(4s^{3}-4s^{2}+5s-5\right)$$

Consider 4s^{3}-4s^{2}+5s-5. Do the grouping 4s^{3}-4s^{2}+5s-5=\left(4s^{3}-4s^{2}\right)+\left(5s-5\right), and factor out 4s^{2} in the first and 5 in the second group.

$$4s^{2}\left(s-1\right)+5\left(s-1\right)$$

Factor out common term s-1 by using distributive property.

$$\left(s-1\right)\left(4s^{2}+5\right)$$

Rewrite the complete factored expression. Polynomial 4s^{2}+5 is not factored since it does not have any rational roots.

$$s\left(s-1\right)\left(4s^{2}+5\right)$$

Evaluate

$$s\left(s-1\right)\left(4s^{2}+5\right)$$