Factor 6x^2-x-12

Problem

6*x2−x−12

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=−1 and c=−12

2. Find two numbers that multiply to a⋅c=6⋅(−12)=−72 and add to b=−1

3. Determine that the two numbers are −9 and 8 since (−9)⋅8=−72 and −9+8=−1

4. Rewrite the middle term −x using these two numbers: 6*x2−9*x+8*x−12

5. Factor by grouping the first two terms and the last two terms: 3*x*(2*x−3)+4*(2*x−3)

6. Factor out the common binomial factor (2*x−3)

Final Answer

6*x2−x−12=(3*x+4)*(2*x−3)

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