Factor 6x^2+7x-20

Problem

6*x2+7*x−20

Solution

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

2. Calculate the product a*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 splitting the expression into two pairs: (6*x2+15*x)+(−8*x−20)

6. Factor out the greatest common factor from each pair.

3*x*(2*x+5)−4*(2*x+5)

7. 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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