Factor 7x^2-13x-2

Problem

7*x2−13*x−2

Solution

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

2. Calculate the product of a and c which is 7⋅(−2)=−14

3. Find two numbers that multiply to −14 and add to the middle coefficient b=−13 These numbers are −14 and 1

4. Rewrite the middle term −13*x using the two numbers found: −14*x+1*x

7*x2−14*x+x−2

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

7*x*(x−2)+1*(x−2)

6. Factor out the common binomial (x−2)

(7*x+1)*(x−2)

Final Answer

7*x2−13*x−2=(7*x+1)*(x−2)

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