Factor 12x^2-3x-9

$12 x^{2} - 3 x - 9$

Step 1

Factor $3$ out of $12 x^{2} - 3 x - 9$ .

Factor $3$ out of $12 x^{2}$ .

$3 (4 x^{2}) - 3 x - 9$

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

$3 (4 x^{2}) + 3 (- x) - 9$

Factor $3$ out of $- 9$ .

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

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

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

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

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

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 $a \cdot c = 4 \cdot - 3 = - 12$ and whose sum is $b = - 1$ .

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

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

Rewrite $- 1$ as $3$ plus $- 4$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$3 (x (4 x + 3) - (4 x + 3))$

Factor the polynomial by factoring out the greatest common factor, $4 x + 3$ .

$3 ((4 x + 3) (x - 1))$

Remove unnecessary parentheses.

$3 (4 x + 3) (x - 1)$

Factor 12x^2-3x-9

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