Solve 10k^3-4k^2+40k-16

$$10 k ^ { 3 } - 4 k ^ { 2 } + 40 k - 16$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(5k^{3}-2k^{2}+20k-8\right)$$

Consider 5k^{3}-2k^{2}+20k-8. Do the grouping 5k^{3}-2k^{2}+20k-8=\left(5k^{3}-2k^{2}\right)+\left(20k-8\right), and factor out k^{2} in the first and 4 in the second group.

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

Factor out common term 5k-2 by using distributive property.

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

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

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

Evaluate

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