Factor 2x^2+11x+12

Problem

2*x2+11*x+12

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=11 and c=12

2. Calculate the product of a and c which is 2⋅12=24

3. Find two numbers that multiply to 24 and add up to the middle coefficient b=11 These numbers are 3 and 8

4. Rewrite the middle term 11*x using the two numbers found: 2*x2+8*x+3*x+12

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 2*x*(x+4)+3*(x+4)

6. Factor out the common binomial (x+4) to obtain the final factored form.

Final Answer

2*x2+11*x+12=(2*x+3)*(x+4)

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