Factor 3x^2+7x-20

Problem

3*x2+7*x−20

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=7 and c=−20

2. Calculate the product of a and c which is 3×−20=−60

3. Find two numbers that multiply to −60 and add to the middle coefficient b=7 These numbers are 12 and −5

4. Rewrite the middle term 7*x using the two numbers found: 12*x−5*x

3*x2+12*x−5*x−20

5. Factor by grouping the first two terms and the last two terms.

3*x*(x+4)−5*(x+4)

6. Factor out the common binomial factor (x+4)

(3*x−5)*(x+4)

Final Answer

3*x2+7*x−20=(3*x−5)*(x+4)

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