Factor 12x^2-7x-12

Problem

12*x2−7*x−12

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=12 b=−7 and c=−12

2. Calculate the product a*c by multiplying 12 and −12

a*c=12⋅(−12)=−144

3. Find two numbers that multiply to −144 and add to the middle coefficient b=−7 These numbers are −16 and 9

4. Rewrite the middle term −7*x using the two numbers found in the previous step.

12*x2−16*x+9*x−12

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

4*x*(3*x−4)+3*(3*x−4)

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

(4*x+3)*(3*x−4)

Final Answer

12*x2−7*x−12=(4*x+3)*(3*x−4)

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