Factor 3x^2+19x+20

Problem

3*x2+19*x+20

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=19 and c=20

2. Calculate the product of a and c which is 3⋅20=60

3. Find two numbers that multiply to 60 and add up to the middle coefficient b=19 These numbers are 15 and 4

4. Rewrite the middle term 19*x using the two numbers found: 15*x+4*x

3*x2+15*x+4*x+20

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

3*x*(x+5)+4*(x+5)

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

(3*x+4)*(x+5)

Final Answer

3*x2+19*x+20=(3*x+4)*(x+5)

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