Solve 12r^3-3r^2+16r-4

$$12 r ^ { 3 } - 3 r ^ { 2 } + 16 r - 4$$

Factor

$$\left(4r-1\right)\left(3r^{2}+4\right)$$

Solution Steps

Do the grouping 12r^{3}-3r^{2}+16r-4=\left(12r^{3}-3r^{2}\right)+\left(16r-4\right), and factor out 3r^{2} in the first and 4 in the second group.

$$3r^{2}\left(4r-1\right)+4\left(4r-1\right)$$

Factor out common term 4r-1 by using distributive property. Polynomial 3r^{2}+4 is not factored since it does not have any rational roots.

$$\left(4r-1\right)\left(3r^{2}+4\right)$$

Evaluate

$$\left(4r-1\right)\left(3r^{2}+4\right)$$