Factor 7x^2-31x-20

Problem

7*x2−31*x−20

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=7 b=−31 and c=−20

2. Calculate the product of a and c which is 7×−20=−140

3. Find two numbers that multiply to −140 and add to the middle coefficient b=−31 These numbers are −35 and 4

4. Rewrite the middle term −31*x using the two numbers found: −35*x+4*x

7*x2−35*x+4*x−20

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

7*x*(x−5)+4*(x−5)

6. Factor out the common binomial (x−5)

(7*x+4)*(x−5)

Final Answer

7*x2−31*x−20=(7*x+4)*(x−5)

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