Solve 7y^3-21y^2+4y-12

$$7 y ^ { 3 } - 21 y ^ { 2 } + 4 y - 12$$

Factor

$$\left(y-3\right)\left(7y^{2}+4\right)$$

Solution Steps

Do the grouping 7y^{3}-21y^{2}+4y-12=\left(7y^{3}-21y^{2}\right)+\left(4y-12\right), and factor out 7y^{2} in the first and 4 in the second group.

$$7y^{2}\left(y-3\right)+4\left(y-3\right)$$

Factor out common term y-3 by using distributive property. Polynomial 7y^{2}+4 is not factored since it does not have any rational roots.

$$\left(y-3\right)\left(7y^{2}+4\right)$$

Evaluate

$$\left(y-3\right)\left(7y^{2}+4\right)$$