Factor 12x^2-x-6

Problem

12*x2−x−6

Solution

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

2. Calculate the product of a and c which is 12⋅−6=−72

3. Find two numbers that multiply to −72 and add to the middle coefficient b=−1 These numbers are −9 and 8

4. Rewrite the middle term −x using the two numbers found: −9*x+8*x

12*x2−9*x+8*x−6

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

3*x*(4*x−3)+2*(4*x−3)

6. Factor out the common binomial (4*x−3)

(3*x+2)*(4*x−3)

Final Answer

12*x2−x−6=(3*x+2)*(4*x−3)

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