Factor 4v^2+15v+9

$4 v^{2} + 15 v + 9$

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 $a \cdot c = 4 \cdot 9 = 36$ and whose sum is $b = 15$ .

Factor $15$ out of $15 v$ .

$4 v^{2} + 15 (v) + 9$

Rewrite $15$ as $3$ plus $12$

$4 v^{2} + (3 + 12) v + 9$

Apply the distributive property.

$4 v^{2} + 3 v + 12 v + 9$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 v^{2} + 3 v) + 12 v + 9$

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

$v (4 v + 3) + 3 (4 v + 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 v + 3$ .

$(4 v + 3) (v + 3)$

Factor 4v^2+15v+9

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