Factor 3v^2+14v+8

$3 v^{2} + 14 v + 8$

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 $a \cdot c = 3 \cdot 8 = 24$ and whose sum is $b = 14$ .

Factor $14$ out of $14 v$ .

$3 v^{2} + 14 (v) + 8$

Rewrite $14$ as $2$ plus $12$

$3 v^{2} + (2 + 12) v + 8$

Apply the distributive property.

$3 v^{2} + 2 v + 12 v + 8$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 v^{2} + 2 v) + 12 v + 8$

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

$v (3 v + 2) + 4 (3 v + 2)$

Step 3

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

$(3 v + 2) (v + 4)$

Factor 3v^2+14v+8

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