Solve 10u^3-12u^2-5u+6

$$10 u ^ { 3 } - 12 u ^ { 2 } - 5 u + 6$$

Factor

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

Solution Steps

Do the grouping 10u^{3}-12u^{2}-5u+6=\left(10u^{3}-12u^{2}\right)+\left(-5u+6\right), and factor out 2u^{2} in the first and -1 in the second group.

$$2u^{2}\left(5u-6\right)-\left(5u-6\right)$$

Factor out common term 5u-6 by using distributive property. Polynomial 2u^{2}-1 is not factored since it does not have any rational roots.

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

Evaluate

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