Factor 12x^2+42x-294

Problem

12*x^2+42*x−294

Solution

1. Factor out the greatest common factor (GCF) from all three terms, which is 6

6*(2*x^2+7*x−49)

2. Identify the coefficients of the quadratic expression inside the parentheses, a*x^2+b*x+c where a=2 b=7 and c=−49

a⋅c=2⋅(−49)=−98

3. Find two numbers that multiply to −98 and add to 7 These numbers are 14 and −7

14⋅(−7)=−98

14+(−7)=7

4. Rewrite the middle term 7*x using the two numbers found in the previous step.

6*(2*x^2+14*x−7*x−49)

5. Factor by grouping the terms inside the parentheses.

6*([[*2*x^2+14*x]]+[[−7*x−49*]])

6. Factor out the GCF from each group.

6*(2*x*(x+7)−7*(x+7))

7. Factor out the common binomial (x+7)

6*(2*x−7)*(x+7)

Final Answer

12*x^2+42*x−294=6*(2*x−7)*(x+7)

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