Factor 3x^2+31x+36

Problem

3*x2+31*x+36

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=31 and c=36

2. Calculate the product a*c by multiplying 3 and 36

a*c=3⋅36=108

3. Find two numbers that multiply to 108 and add up to the middle coefficient b=31

27⋅4=108

27+4=31

4. Rewrite the middle term 31*x using the two numbers found in the previous step.

3*x2+27*x+4*x+36

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

3*x*(x+9)+4*(x+9)

6. Factor out the common binomial (x+9) to obtain the final factored form.

(3*x+4)*(x+9)

Final Answer

3*x2+31*x+36=(3*x+4)*(x+9)

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