Factor 12x^2-5x-2

Problem

12*x2−5*x−2

Solution

1. Identify the coefficients a b and c from the quadratic expression a*x2+b*x+c where a=12 b=−5 and c=−2

2. Calculate the product a*c which is 12×−2=−24

3. Find two numbers that multiply to −24 and add to the middle coefficient b=−5 These numbers are −8 and 3

4. Rewrite the middle term −5*x using the two numbers found: 12*x2−8*x+3*x−2

5. Factor by grouping the first two terms and the last two terms: (12*x2−8*x)+(3*x−2)

6. Factor out the greatest common factor from each group: 4*x*(3*x−2)+1*(3*x−2)

7. Factor out the common binomial (3*x−2) to obtain the final factored form.

Final Answer

12*x2−5*x−2=(4*x+1)*(3*x−2)

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