Factor 4x^2+15x+9

Problem

4*x2+15*x+9

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=15 and c=9

2. Calculate the product a*c which is 4⋅9=36

3. Find two numbers that multiply to 36 and add 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

4*x2+12*x+3*x+9

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

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

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

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

Final Answer

4*x2+15*x+9=(4*x+3)*(x+3)

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