Factor 9x^2+15x+4

Problem

9*x2+15*x+4

Solution

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

2. Find two numbers that multiply to a⋅c=9⋅4=36 and add to b=15

3. Determine the pair of numbers, which are 12 and 3 since 12⋅3=36 and 12 + 3 = 15$.

4. Rewrite the middle term 15*x using the two numbers found: 9*x2+12*x+3*x+4

5. Factor by grouping the first two terms and the last two terms: (9*x2+12*x)+(3*x+4)

6. Factor out the greatest common factor from each group: 3*x*(3*x+4)+1*(3*x+4)

7. Factor out the common binomial (3*x+4) to obtain the final factored form.

Final Answer

9*x2+15*x+4=(3*x+4)*(3*x+1)

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