Factor 12y^2-4y-5

$12 y^{2} - 4 y - 5$

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 $a \cdot c = 12 \cdot - 5 = - 60$ and whose sum is $b = - 4$ .

Factor $- 4$ out of $- 4 y$ .

$12 y^{2} - 4 (y) - 5$

Rewrite $- 4$ as $6$ plus $- 10$

$12 y^{2} + (6 - 10) y - 5$

Apply the distributive property.

$12 y^{2} + 6 y - 10 y - 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 y^{2} + 6 y) - 10 y - 5$

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

$6 y (2 y + 1) - 5 (2 y + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 y + 1$ .

$(2 y + 1) (6 y - 5)$

Factor 12y^2-4y-5

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