Factor 2x^3+x^2-8x-4

$2 x^{3} + x^{2} - 8 x - 4$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{3} + x^{2}) - 8 x - 4$

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

$x^{2} (2 x + 1) - 4 (2 x + 1)$

Step 2

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

$(2 x + 1) (x^{2} - 4)$

Step 3

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

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

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 $b = 2$ .

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

Remove unnecessary parentheses.

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