Factor 2y^2+3y-9

$2 y^{2} + 3 y - 9$

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 $a \cdot c = 2 \cdot - 9 = - 18$ and whose sum is $b = 3$ .

Factor $3$ out of $3 y$ .

$2 y^{2} + 3 (y) - 9$

Rewrite $3$ as $- 3$ plus $6$

$2 y^{2} + (- 3 + 6) y - 9$

Apply the distributive property.

$2 y^{2} - 3 y + 6 y - 9$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 y^{2} - 3 y) + 6 y - 9$

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

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

Step 3

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

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

Factor 2y^2+3y-9

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