Factor 6x^2-7x-20

Problem

6*x2−7*x−20

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=6 b=−7 and c=−20

2. Calculate the product of a and c which is 6×−20=−120

3. Find two numbers that multiply to −120 and add to the middle coefficient b=−7 These numbers are −15 and 8

4. Rewrite the middle term −7*x using the two numbers found: −15*x+8*x

6*x2−15*x+8*x−20

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

3*x*(2*x−5)+4*(2*x−5)

6. Factor out the common binomial (2*x−5)

(3*x+4)*(2*x−5)

Final Answer

6*x2−7*x−20=(3*x+4)*(2*x−5)

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