Factor by Grouping 12x^2-13x-4

$12 x^{2} - 13 x - 4$

Step 1

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 $a \cdot c = 12 \cdot - 4 = - 48$ and whose sum is $b = - 13$ .

Factor $- 13$ out of $- 13 x$ .

$12 x^{2} - 13 (x) - 4$

Rewrite $- 13$ as $3$ plus $- 16$

$12 x^{2} + (3 - 16) x - 4$

Apply the distributive property.

$12 x^{2} + 3 x - 16 x - 4$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} + 3 x) - 16 x - 4$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

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

Factor by Grouping 12x^2-13x-4

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