Solve 4r^3+14r^2-2r-7

$$4 r ^ { 3 } + 14 r ^ { 2 } - 2 r - 7$$

Factor

$$\left(2r+7\right)\left(2r^{2}-1\right)$$

Solution Steps

Do the grouping 4r^{3}+14r^{2}-2r-7=\left(4r^{3}+14r^{2}\right)+\left(-2r-7\right), and factor out 2r^{2} in the first and -1 in the second group.

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

Factor out common term 2r+7 by using distributive property. Polynomial 2r^{2}-1 is not factored since it does not have any rational roots.

$$\left(2r+7\right)\left(2r^{2}-1\right)$$

Evaluate

$$\left(2r+7\right)\left(2r^{2}-1\right)$$