Factor 24x^2-4x-4

$24 x^{2} - 4 x - 4$

Step 1

Factor $4$ out of $24 x^{2} - 4 x - 4$ .

Factor $4$ out of $24 x^{2}$ .

$4 (6 x^{2}) - 4 x - 4$

Factor $4$ out of $- 4 x$ .

$4 (6 x^{2}) + 4 (- x) - 4$

Factor $4$ out of $- 4$ .

$4 (6 x^{2}) + 4 (- x) + 4 (- 1)$

Factor $4$ out of $4 (6 x^{2}) + 4 (- x)$ .

$4 (6 x^{2} - x) + 4 (- 1)$

Factor $4$ out of $4 (6 x^{2} - x) + 4 (- 1)$ .

$4 (6 x^{2} - x - 1)$

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 $a \cdot c = 6 \cdot - 1 = - 6$ and whose sum is $b = - 1$ .

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

$4 (6 x^{2} - (x) - 1)$

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

$4 (6 x^{2} + (2 - 3) x - 1)$

Apply the distributive property.

$4 (6 x^{2} + 2 x - 3 x - 1)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$4 ((6 x^{2} + 2 x) - 3 x - 1)$

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

$4 (2 x (3 x + 1) - (3 x + 1))$

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$4 ((3 x + 1) (2 x - 1))$

Remove unnecessary parentheses.

$4 (3 x + 1) (2 x - 1)$

Factor 24x^2-4x-4

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