Factor 6x^3-18x^2-2x+6

$6 x^{3} - 18 x^{2} - 2 x + 6$

Step 1

Factor $2$ out of $6 x^{3} - 18 x^{2} - 2 x + 6$ .

Factor $2$ out of $6 x^{3}$ .

$2 (3 x^{3}) - 18 x^{2} - 2 x + 6$

Factor $2$ out of $- 18 x^{2}$ .

$2 (3 x^{3}) + 2 (- 9 x^{2}) - 2 x + 6$

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

$2 (3 x^{3}) + 2 (- 9 x^{2}) + 2 (- x) + 6$

Factor $2$ out of $6$ .

$2 (3 x^{3}) + 2 (- 9 x^{2}) + 2 (- x) + 2 (3)$

Factor $2$ out of $2 (3 x^{3}) + 2 (- 9 x^{2})$ .

$2 (3 x^{3} - 9 x^{2}) + 2 (- x) + 2 (3)$

Factor $2$ out of $2 (3 x^{3} - 9 x^{2}) + 2 (- x)$ .

$2 (3 x^{3} - 9 x^{2} - x) + 2 (3)$

Factor $2$ out of $2 (3 x^{3} - 9 x^{2} - x) + 2 (3)$ .

$2 (3 x^{3} - 9 x^{2} - x + 3)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((3 x^{3} - 9 x^{2}) - x + 3)$

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

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

Step 3

Factor.

Factor the polynomial by factoring out the greatest common factor, $x - 3$ .

$2 ((x - 3) (3 x^{2} - 1))$

Remove unnecessary parentheses.

$2 (x - 3) (3 x^{2} - 1)$