Factor 10x^2+19x+6

Problem

10*x2+19*x+6

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=10 b=19 and c=6

2. Calculate the product of a and c which is 10⋅6=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

10*x2+15*x+4*x+6

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

5*x*(2*x+3)+2*(2*x+3)

6. Factor out the common binomial (2*x+3)

(5*x+2)*(2*x+3)

Final Answer

10*x2+19*x+6=(5*x+2)*(2*x+3)

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