Factor 2x^2+13x-7

Problem

2*x2+13*x−7

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=13 and c=−7

2. Find two numbers that multiply to a⋅c=2⋅(−7)=−14 and add to b=13

3. Determine the pair of numbers, which are 14 and −1 since 14⋅(−1)=−14 and 14 + (-1) = 13$.

4. Rewrite the middle term 13*x using these two numbers: 14*x−x

2*x2+14*x−x−7

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

2*x*(x+7)−1*(x+7)

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

(2*x−1)*(x+7)

Final Answer

2*x2+13*x−7=(2*x−1)*(x+7)

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