Solve 8p^3-32p^2+28p-112

$$8 p ^ { 3 } - 32 p ^ { 2 } + 28 p - 112$$

Factor

$$4\left(p-4\right)\left(2p^{2}+7\right)$$

Solution Steps

Factor out 4.

$$4\left(2p^{3}-8p^{2}+7p-28\right)$$

Consider 2p^{3}-8p^{2}+7p-28. Do the grouping 2p^{3}-8p^{2}+7p-28=\left(2p^{3}-8p^{2}\right)+\left(7p-28\right), and factor out 2p^{2} in the first and 7 in the second group.

$$2p^{2}\left(p-4\right)+7\left(p-4\right)$$

Factor out common term p-4 by using distributive property.

$$\left(p-4\right)\left(2p^{2}+7\right)$$

Rewrite the complete factored expression. Polynomial 2p^{2}+7 is not factored since it does not have any rational roots.

$$4\left(p-4\right)\left(2p^{2}+7\right)$$

Evaluate

$$4\left(p-4\right)\left(2p^{2}+7\right)$$