Factor 6x^2+13x+6

Problem

6*x2+13*x+6

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=6 b=13 and c=6

2. Calculate the product of a and c which is 6⋅6=36

3. Find two numbers that multiply to 36 and add up to the middle coefficient b=13 These numbers are 4 and 9

4. Rewrite the middle term 13*x using the two numbers found: 4*x+9*x

6*x2+4*x+9*x+6

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

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

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

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

Final Answer

6*x2+13*x+6=(3*x+2)*(2*x+3)

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