Factor 2x^2+11x+15

Problem

2*x2+11*x+15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=11 and c=15

2. Calculate the product of a and c which is 2⋅15=30

3. Find two numbers that multiply to 30 and add up to the middle coefficient b=11 These numbers are 5 and 6

4. Rewrite the middle term 11*x using the two numbers found: 2*x2+6*x+5*x+15

5. Factor by grouping the first two terms and the last two terms: 2*x*(x+3)+5*(x+3)

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

Final Answer

2*x2+11*x+15=(2*x+5)*(x+3)

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