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. Multiply the leading coefficient a and the constant term c to find the product a*c

2⋅−7=−14

3. Find two numbers that multiply to −14 and add to the middle coefficient b=−13

−14⋅1=−14

−14+1=−13

4. Rewrite the middle term −13*x using the two numbers found in the previous step.

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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