Solve 7v^3+2v^2-35v-10

$$7 v ^ { 3 } + 2 v ^ { 2 } - 35 v - 10$$

Factor

$$\left(7v+2\right)\left(v^{2}-5\right)$$

Solution Steps

Do the grouping 7v^{3}+2v^{2}-35v-10=\left(7v^{3}+2v^{2}\right)+\left(-35v-10\right), and factor out v^{2} in the first and -5 in the second group.

$$v^{2}\left(7v+2\right)-5\left(7v+2\right)$$

Factor out common term 7v+2 by using distributive property. Polynomial v^{2}-5 is not factored since it does not have any rational roots.

$$\left(7v+2\right)\left(v^{2}-5\right)$$

Evaluate

$$\left(7v+2\right)\left(v^{2}-5\right)$$