Factor 5n^2+19n+12

Problem

5*n2+19*n+12

Solution

1. Identify the coefficients of the quadratic expression a*n2+b*n+c where a=5 b=19 and c=12

2. Find two numbers that multiply to a⋅c=5⋅12=60 and add to b=19

3. Determine the pair of numbers, which are 15 and 4 since 15⋅4=60 and 15 + 4 = 19$.

4. Rewrite the middle term 19*n using these two numbers as 15*n+4*n

5*n2+15*n+4*n+12

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

5*n*(n+3)+4*(n+3)

6. Factor out the common binomial (n+3)

(5*n+4)*(n+3)

Final Answer

5*n2+19*n+12=(5*n+4)*(n+3)

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