Factor 2y^2+9y+10

$2 y^{2} + 9 y + 10$

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 $a \cdot c = 2 \cdot 10 = 20$ and whose sum is $b = 9$ .

Factor $9$ out of $9 y$ .

$2 y^{2} + 9 (y) + 10$

Rewrite $9$ as $4$ plus $5$

$2 y^{2} + (4 + 5) y + 10$

Apply the distributive property.

$2 y^{2} + 4 y + 5 y + 10$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 y^{2} + 4 y) + 5 y + 10$

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

$2 y (y + 2) + 5 (y + 2)$

Step 3

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

$(y + 2) (2 y + 5)$

Factor 2y^2+9y+10

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