Factor 9x^2-3x-6

$9 x^{2} - 3 x - 6$

Step 1

Factor $3$ out of $9 x^{2} - 3 x - 6$ .

Factor $3$ out of $9 x^{2}$ .

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

Factor $3$ out of $- 3 x$ .

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

Factor $3$ out of $- 6$ .

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

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

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

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

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

Step 2

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 2 = - 6$ and whose sum is $b = - 1$ .

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

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

Rewrite $- 1$ as $2$ plus $- 3$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$3 (x (3 x + 2) - (3 x + 2))$

Factor the polynomial by factoring out the greatest common factor, $3 x + 2$ .

$3 ((3 x + 2) (x - 1))$

Remove unnecessary parentheses.

$3 (3 x + 2) (x - 1)$

Factor 9x^2-3x-6

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