Factor 2x^3+x^2-72x-36

$2 x^{3} + x^{2} - 72 x - 36$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{3} + x^{2}) - 72 x - 36$

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

$x^{2} (2 x + 1) - 36 (2 x + 1)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$(2 x + 1) (x^{2} - 36)$

Step 3

Rewrite $36$ as $6^{2}$ .

$(2 x + 1) (x^{2} - 6^{2})$

Step 4

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 6$ .

$(2 x + 1) ((x + 6) (x - 6))$

Remove unnecessary parentheses.

$(2 x + 1) (x + 6) (x - 6)$