Factor 3x^2-16x-12

Problem

3*x2−16*x−12

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−16 and c=−12

2. Calculate the product of a and c which is 3×−12=−36

3. Find two numbers that multiply to −36 and add to the middle coefficient b=−16 These numbers are −18 and 2

4. Rewrite the middle term −16*x using the two numbers found: −18*x+2*x

3*x2−18*x+2*x−12

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

3*x*(x−6)+2*(x−6)

6. Factor out the common binomial (x−6)

(3*x+2)*(x−6)

Final Answer

3*x2−16*x−12=(3*x+2)*(x−6)

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