Factor 2v^2+9v+9

$2 v^{2} + 9 v + 9$

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 $b = 9$ .

Factor $9$ out of $9 v$ .

$2 v^{2} + 9 (v) + 9$

Rewrite $9$ as $3$ plus $6$

$2 v^{2} + (3 + 6) v + 9$

Apply the distributive property.

$2 v^{2} + 3 v + 6 v + 9$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 v^{2} + 3 v) + 6 v + 9$

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

$v (2 v + 3) + 3 (2 v + 3)$

Step 3

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

$(2 v + 3) (v + 3)$

Factor 2v^2+9v+9

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