Factor 2y^2+9y-18

$2 y^{2} + 9 y - 18$

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 $a \cdot c = 2 \cdot - 18 = - 36$ and whose sum is $b = 9$ .

Factor $9$ out of $9 y$ .

$2 y^{2} + 9 (y) - 18$

Rewrite $9$ as $- 3$ plus $12$

$2 y^{2} + (- 3 + 12) y - 18$

Apply the distributive property.

$2 y^{2} - 3 y + 12 y - 18$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 y^{2} - 3 y) + 12 y - 18$

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

$y (2 y - 3) + 6 (2 y - 3)$

Step 3

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

$(2 y - 3) (y + 6)$

Factor 2y^2+9y-18

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