Factor 3x^2-20x-7

Problem

3*x2−20*x−7

Solution

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

2. Calculate the product of a and c which is 3×−7=−21

3. Find two numbers that multiply to −21 and add to the middle coefficient b=−20 These numbers are −21 and 1

4. Rewrite the middle term −20*x using the two numbers found: 3*x2−21*x+x−7

5. Factor by grouping the first two terms and the last two terms: 3*x*(x−7)+1*(x−7)

6. Factor out the common binomial factor (x−7)

Final Answer

3*x2−20*x−7=(3*x+1)*(x−7)

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