Factor 6x^2+7x-49

Problem

6*x2+7*x−49

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=7 and c=−49

2. Calculate the product a*c by multiplying 6 and −49 which results in −294

3. Find two numbers that multiply to −294 and add to the middle coefficient b=7 These numbers are 21 and −14

4. Rewrite the middle term 7*x using the two numbers found: 21*x−14*x

6*x2+21*x−14*x−49

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

3*x*(2*x+7)−7*(2*x+7)

6. Factor out the common binomial factor (2*x+7)

(3*x−7)*(2*x+7)

Final Answer

6*x2+7*x−49=(3*x−7)*(2*x+7)

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