Factor 2y^2-y-15

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

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 $b = - 1$ .

Factor $- 1$ out of $- y$ .

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

Rewrite $- 1$ as $5$ plus $- 6$

$2 y^{2} + (5 - 6) y - 15$

Apply the distributive property.

$2 y^{2} + 5 y - 6 y - 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 y^{2} + 5 y) - 6 y - 15$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 y + 5$ .

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

Factor 2y^2-y-15

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