Factor 2x^2+9x+7

Problem

2*x2+9*x+7

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=9 and c=7

2. Find two numbers that multiply to a⋅c=14 and add to b=9

3. Determine the pair of numbers, which are 2 and 7 since 2⋅7=14 and 2 + 7 = 9$.

4. Rewrite the middle term 9*x using the pair found: 2*x2+2*x+7*x+7

5. Factor by grouping the first two terms and the last two terms: (2*x2+2*x)+(7*x+7)

6. Factor out the greatest common factor from each group: 2*x*(x+1)+7*(x+1)

7. Factor out the common binomial (x+1) to obtain the final factored form.

Final Answer

2*x2+9*x+7=(2*x+7)*(x+1)

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