Solve 20k^3-20k^2-8k+8

$$20 k ^ { 3 } - 20 k ^ { 2 } - 8 k + 8$$

Factor

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

Solution Steps

Factor out 4.

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

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

$$5k^{2}\left(k-1\right)-2\left(k-1\right)$$

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

$$\left(k-1\right)\left(5k^{2}-2\right)$$

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

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

Evaluate

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