Factor 9x^2+24x+15

Problem

9*x2+24*x+15

Solution

1. Factor out the greatest common factor (GCF) of the three terms, which is 3

3*(3*x2+8*x+5)

2. Identify the coefficients of the quadratic expression inside the parentheses, 3*x2+8*x+5 where a=3 b=8 and c=5

3. Find two numbers that multiply to a*c=3⋅5=15 and add to b=8 These numbers are 3 and 5

4. Rewrite the middle term 8*x using the numbers found in the previous step.

3*(3*x2+3*x+5*x+5)

5. Factor by grouping the terms inside the parentheses.

3*((3*x2+3*x)+(5*x+5))

6. Extract the common factors from each group.

3*(3*x*(x+1)+5*(x+1))

7. Factor out the common binomial (x+1)

3*(3*x+5)*(x+1)

Final Answer

9*x2+24*x+15=3*(3*x+5)*(x+1)

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