Factor 2v^2+11v+5

Problem

2*v2+11*v+5

Solution

1. Identify the coefficients of the quadratic expression in the form a*v2+b*v+c where a=2 b=11 and c=5

2. Find two numbers that multiply to a⋅c=10 and add to b=11

3. Determine the pair of numbers, which are 10 and 1 since 10⋅1=10 and 10 + 1 = 11$.

4. Rewrite the middle term 11*v using these two numbers as 10*v+v

2*v2+10*v+v+5

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

2*v*(v+5)+1*(v+5)

6. Factor out the common binomial (v+5)

(2*v+1)*(v+5)

Final Answer

2*v2+11*v+5=(2*v+1)*(v+5)

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