Question

factor completely.
$2v^{2}+13v + 11$

Explanation:

Step1: Find two numbers that multiply to \(2\times11 = 22\) and add up to \(13\).

The numbers are \(11\) and \(2\) since \(11\times2 = 22\) and \(11 + 2=13\).

Step2: Rewrite the middle term using these two numbers.

\(2v^{2}+2v + 11v+11\)

Step3: Group the terms and factor out the greatest common factor (GCF) from each group.

\((2v^{2}+2v)+(11v + 11)=2v(v + 1)+11(v + 1)\)

Step4: Factor out the common binomial factor \((v + 1)\).

\((2v + 11)(v + 1)\)

Answer:

\((2v + 11)(v + 1)\)