Solve 2v^3-8v^2-3v+12

$$2 v ^ { 3 } - 8 v ^ { 2 } - 3 v + 12$$

Factor

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

Solution Steps

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

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

Factor out common term v-4 by using distributive property. Polynomial 2v^{2}-3 is not factored since it does not have any rational roots.

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

Evaluate

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