Factor 6x^2+19x+10

Problem

6*x2+19*x+10

Solution

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

2. Calculate the product of a and c which is 6⋅10=60

3. Find two numbers that multiply to 60 and add 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

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

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

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

6. Factor out the common binomial factor (2*x+5)

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

Final Answer

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

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