Factor 9x^2+9x+2

Problem

9*x2+9*x+2

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=9 b=9 and c=2

2. Find two numbers that multiply to a⋅c=18 and add to b=9

3. Determine that the two numbers are 6 and 3 since 6⋅3=18 and 6 + 3 = 9$.

4. Rewrite the middle term 9*x using these two numbers: 9*x2+6*x+3*x+2

5. Factor by grouping the first two terms and the last two terms: 3*x*(3*x+2)+1*(3*x+2)

6. Factor out the common binomial factor (3*x+2)

Final Answer

9*x2+9*x+2=(3*x+2)*(3*x+1)

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