Factor 6x^2+37x+6

Problem

6*x2+37*x+6

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=6 b=37 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=37 These numbers are 36 and 1

4. Rewrite the middle term 37*x using the two numbers found: 36*x+1*x

6*x2+36*x+x+6

5. Factor by grouping the first two terms and the last two terms.

(6*x2+36*x)+(x+6)

6. Factor out the greatest common factor from each group.

6*x*(x+6)+1*(x+6)

7. Extract the common binomial factor (x+6)

(6*x+1)*(x+6)

Final Answer

6*x2+37*x+6=(6*x+1)*(x+6)

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