Factor 2v^2+11v+5 - MathMaster

$2 v^{2} + 11 v + 5$

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 $a \cdot c = 2 \cdot 5 = 10$ and whose sum is $b = 11$ .

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Factor $11$ out of $11 v$ .

$2 v^{2} + 11 (v) + 5$

Rewrite $11$ as $1$ plus $10$

$2 v^{2} + (1 + 10) v + 5$

Apply the distributive property.

$2 v^{2} + 1 v + 10 v + 5$

Multiply $v$ by $1$ .

$2 v^{2} + v + 10 v + 5$

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

$(2 v^{2} + v) + 10 v + 5$

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

$v (2 v + 1) + 5 (2 v + 1)$

Factor the polynomial by factoring out the greatest common factor, $2 v + 1$ .

$(2 v + 1) (v + 5)$

Factor 2v^2+11v+5

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