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

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

Factor

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

Solution Steps

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

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

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

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

Evaluate

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