Solve 2s^3-27-18s+3s^2

$$2 s ^ { 3 } - 27 - 18 s + 3 s ^ { 2 }$$

Factor

$$\left(s-3\right)\left(s+3\right)\left(2s+3\right)$$

Solution Steps

Do the grouping 2s^{3}-27-18s+3s^{2}=\left(2s^{3}+3s^{2}\right)+\left(-18s-27\right), and factor out s^{2} in the first and -9 in the second group.

$$s^{2}\left(2s+3\right)-9\left(2s+3\right)$$

Factor out common term 2s+3 by using distributive property.

$$\left(2s+3\right)\left(s^{2}-9\right)$$

Consider s^{2}-9. Rewrite s^{2}-9 as s^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(s-3\right)\left(s+3\right)$$

Rewrite the complete factored expression.

$$\left(s-3\right)\left(s+3\right)\left(2s+3\right)$$

Evaluate

$$\left(2s+3\right)\left(s^{2}-9\right)$$