Factor 2x^2+15x+18

Problem

2*x2+15*x+18

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=15 and c=18

2. Calculate the product of a and c which is 2⋅18=36

3. Find two numbers that multiply to 36 and add up to the middle coefficient b=15 These numbers are 12 and 3

4. Rewrite the middle term 15*x using the two numbers found: 12*x+3*x

2*x2+12*x+3*x+18

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

2*x*(x+6)+3*(x+6)

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

(2*x+3)*(x+6)

Final Answer

2*x2+15*x+18=(2*x+3)*(x+6)

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