Factor 2x^2+15x+7

Problem

2*x2+15*x+7

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=15 and c=7

2. Find two numbers that multiply to a⋅c=2⋅7=14 and add to b=15

3. Determine the pair of numbers, which are 14 and 1 since 14⋅1=14 and 14 + 1 = 15$.

4. Rewrite the middle term 15*x using the two numbers found: 2*x2+14*x+x+7

5. Factor by grouping the first two terms and the last two terms: 2*x*(x+7)+1*(x+7)

6. Factor out the common binomial factor (x+7)

Final Answer

2*x2+15*x+7=(2*x+1)*(x+7)

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