Factor 7x^2-45x-28

Problem

7*x2−45*x−28

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=7 b=−45 and c=−28

2. Calculate the product of a and c which is 7×−28=−196

3. Find two numbers that multiply to −196 and add to the middle coefficient b=−45 These numbers are −49 and 4

4. Rewrite the middle term −45*x using the two numbers found: −49*x+4*x

7*x2−49*x+4*x−28

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

7*x*(x−7)+4*(x−7)

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

(7*x+4)*(x−7)

Final Answer

7*x2−45*x−28=(7*x+4)*(x−7)

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