Solve 3z^3+2z-12z^2-8=

$$3 z ^ { 3 } + 2 z - 12 z ^ { 2 } - 8 =$$

Factor

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

Solution Steps

Do the grouping 3z^{3}+2z-12z^{2}-8=\left(3z^{3}+2z\right)+\left(-12z^{2}-8\right), and factor out z in the first and -4 in the second group.

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

Factor out common term 3z^{2}+2 by using distributive property. Polynomial 3z^{2}+2 is not factored since it does not have any rational roots.

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

Evaluate

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