Factor over the Complex Numbers 2x^3-4x^2-38x+76

$2 x^{3} - 4 x^{2} - 38 x + 76$

Step 1

Factor $2$ out of $2 x^{3} - 4 x^{2} - 38 x + 76$ .

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

$2 (x^{3}) - 4 x^{2} - 38 x + 76$

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

$2 (x^{3}) + 2 (- 2 x^{2}) - 38 x + 76$

Factor $2$ out of $- 38 x$ .

$2 (x^{3}) + 2 (- 2 x^{2}) + 2 (- 19 x) + 76$

Factor $2$ out of $76$ .

$2 x^{3} + 2 (- 2 x^{2}) + 2 (- 19 x) + 2 \cdot 38$

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

$2 (x^{3} - 2 x^{2}) + 2 (- 19 x) + 2 \cdot 38$

Factor $2$ out of $2 (x^{3} - 2 x^{2}) + 2 (- 19 x)$ .

$2 (x^{3} - 2 x^{2} - 19 x) + 2 \cdot 38$

Factor $2$ out of $2 (x^{3} - 2 x^{2} - 19 x) + 2 \cdot 38$ .

$2 (x^{3} - 2 x^{2} - 19 x + 38)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((x^{3} - 2 x^{2}) - 19 x + 38)$

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

$2 (x^{2} (x - 2) - 19 (x - 2))$

Step 3

Factor.

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

$2 ((x - 2) (x^{2} - 19))$

Remove unnecessary parentheses.

$2 (x - 2) (x^{2} - 19)$