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

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

Factor $2$ out of $- 2 x^{3} - 4 x^{2} + 2 x + 4$ .

Factor $2$ out of $- 2 x^{3}$ .

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

Factor $2$ out of $- 4 x^{2}$ .

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

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $4$ .

$2 (- x^{3}) + 2 (- 2 x^{2}) + 2 x + 2 \cdot 2$

Factor $2$ out of $2 (- x^{3}) + 2 (- 2 x^{2})$ .

$2 (- x^{3} - 2 x^{2}) + 2 x + 2 \cdot 2$

Factor $2$ out of $2 (- x^{3} - 2 x^{2}) + 2 x$ .

$2 (- x^{3} - 2 x^{2} + x) + 2 \cdot 2$

Factor $2$ out of $2 (- x^{3} - 2 x^{2} + x) + 2 \cdot 2$ .

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Rewrite $1$ as $1^{2}$ .

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

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Factor.

Factor $- 1$ out of $- x - 2$ .

Factor $- 1$ out of $- x$ .

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

Rewrite $- 2$ as $- 1 (2)$ .

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

Factor $- 1$ out of $- (x) - 1 (2)$ .

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

Remove unnecessary parentheses.

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

Multiply $2$ by $- 1$ .

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