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

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

Reorder terms.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $2 s + 3$ .

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

Rewrite $9$ as $3^{2}$ .

$(2 s + 3) (s^{2} - 3^{2})$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = s$ and $b = 3$ .

$(2 s + 3) ((s + 3) (s - 3))$

Remove unnecessary parentheses.

$(2 s + 3) (s + 3) (s - 3)$