Factor 2y^2-7y-15

$2 y^{2} - 7 y - 15$

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 $a \cdot c = 2 \cdot - 15 = - 30$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 y$ .

$2 y^{2} - 7 (y) - 15$

Rewrite $- 7$ as $3$ plus $- 10$

$2 y^{2} + (3 - 10) y - 15$

Apply the distributive property.

$2 y^{2} + 3 y - 10 y - 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 y^{2} + 3 y) - 10 y - 15$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 y + 3$ .

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

Factor 2y^2-7y-15

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