Write as a Set of Linear Factors f(x)=2x^3+4x^2-2x-4

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

Step 1

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

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

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

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

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

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

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

Factor $2$ out of $- 4$ .

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

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

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

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

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

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

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$f (x) = 2 (x^{2} (x + 2) - (x + 2))$

Step 3

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

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

Step 4

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

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

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 $a = x$ and $b = 1$ .

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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