Factor 2x^2+9x+9

Problem

2*x2+9*x+9

Solution

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

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

3. Determine the pair of numbers, which are 3 and 6 since 3⋅6=18 and 3 + 6 = 9$.

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

2*x2+6*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.

2*x*(x+3)+3*(x+3)

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

(2*x+3)*(x+3)

Final Answer

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

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