Factor 3x^2-7x-20

Problem

3*x2−7*x−20

Solution

1. Identify the coefficients of the quadratic expression in the form 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: 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 (x−4) to obtain the final factored form.

Final Answer

3*x2−7*x−20=(3*x+5)*(x−4)

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