Factor 12x^2+6x-6

Problem

12*x2+6*x−6

Solution

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

6*(2*x2+x−1)

2. Identify the coefficients of the quadratic expression inside the parentheses, a*x2+b*x+c where a=2 b=1 and c=−1

a⋅c=2⋅−1=−2

3. Find two numbers that multiply to −2 and add to 1 These numbers are 2 and −1

2⋅−1=−2

2+(−1)=1

4. Split the middle term x using the numbers found in the previous step.

6*(2*x2+2*x−x−1)

5. Factor by grouping the terms inside the parentheses.

6*(2*x*(x+1)−1*(x+1))

6. Factor out the common binomial (x+1)

6*(2*x−1)*(x+1)

Final Answer

12*x2+6*x−6=6*(2*x−1)*(x+1)

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