Factor 7x^2-20x-3

Problem

7*x2−20*x−3

Solution

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

2. Calculate the product of a and c which is 7×−3=−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: −21*x+1*x

7*x2−21*x+x−3

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

7*x*(x−3)+1*(x−3)

6. Factor out the common binomial factor (x−3)

(7*x+1)*(x−3)

Final Answer

7*x2−20*x−3=(7*x+1)*(x−3)

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