Factor 18h^3+45h^2-8h-20

$18 h^{3} + 45 h^{2} - 8 h - 20$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(18 h^{3} + 45 h^{2}) - 8 h - 20$

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

$9 h^{2} (2 h + 5) - 4 (2 h + 5)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $2 h + 5$ .

$(2 h + 5) (9 h^{2} - 4)$

Step 3

Rewrite $9 h^{2}$ as ${(3 h)}^{2}$ .

$(2 h + 5) ({(3 h)}^{2} - 4)$

Step 4

Rewrite $4$ as $2^{2}$ .

$(2 h + 5) ({(3 h)}^{2} - 2^{2})$

Step 5

Factor.

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

$(2 h + 5) ((3 h + 2) (3 h - 2))$

Remove unnecessary parentheses.

$(2 h + 5) (3 h + 2) (3 h - 2)$