Solve 12r^3+2r^2-60r-10

$$12 r ^ { 3 } + 2 r ^ { 2 } - 60 r - 10$$

Factor

$$2\left(6r+1\right)\left(r^{2}-5\right)$$

Solution Steps

Factor out 2.

$$2\left(6r^{3}+r^{2}-30r-5\right)$$

Consider 6r^{3}+r^{2}-30r-5. Do the grouping 6r^{3}+r^{2}-30r-5=\left(6r^{3}+r^{2}\right)+\left(-30r-5\right), and factor out r^{2} in the first and -5 in the second group.

$$r^{2}\left(6r+1\right)-5\left(6r+1\right)$$

Factor out common term 6r+1 by using distributive property.

$$\left(6r+1\right)\left(r^{2}-5\right)$$

Rewrite the complete factored expression. Polynomial r^{2}-5 is not factored since it does not have any rational roots.

$$2\left(6r+1\right)\left(r^{2}-5\right)$$

Evaluate

$$2\left(6r+1\right)\left(r^{2}-5\right)$$