Factor 6y^2+7y-20

$6 y^{2} + 7 y - 20$

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 $a \cdot c = 6 \cdot - 20 = - 120$ and whose sum is $b = 7$ .

Factor $7$ out of $7 y$ .

$6 y^{2} + 7 (y) - 20$

Rewrite $7$ as $- 8$ plus $15$

$6 y^{2} + (- 8 + 15) y - 20$

Apply the distributive property.

$6 y^{2} - 8 y + 15 y - 20$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 y^{2} - 8 y) + 15 y - 20$

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

$2 y (3 y - 4) + 5 (3 y - 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 y - 4$ .

$(3 y - 4) (2 y + 5)$

Factor 6y^2+7y-20

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