Factor 12y^2-5y-2

$12 y^{2} - 5 y - 2$

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 $a \cdot c = 12 \cdot - 2 = - 24$ and whose sum is $b = - 5$ .

Factor $- 5$ out of $- 5 y$ .

$12 y^{2} - 5 (y) - 2$

Rewrite $- 5$ as $3$ plus $- 8$

$12 y^{2} + (3 - 8) y - 2$

Apply the distributive property.

$12 y^{2} + 3 y - 8 y - 2$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 y^{2} + 3 y) - 8 y - 2$

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

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

Step 3

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

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

Factor 12y^2-5y-2

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