Factor 2n^2+5n+2

Problem

2*n2+5*n+2

Solution

1. Identify the coefficients of the quadratic expression a*n2+b*n+c where a=2 b=5 and c=2

2. Find two numbers that multiply to a*c=2⋅2=4 and add to b=5 These numbers are 4 and 1

3. Rewrite the middle term 5*n using the two numbers found: 4*n+n

2*n2+4*n+n+2

4. Factor by grouping the first two terms and the last two terms.

(2*n2+4*n)+(n+2)

5. Factor out the greatest common factor from each group.

2*n*(n+2)+1*(n+2)

6. Factor out the common binomial (n+2)

(2*n+1)*(n+2)

Final Answer

2*n2+5*n+2=(2*n+1)*(n+2)

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