Factor 12x^2-25x+12

Problem

12*x2−25*x+12

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=12 b=−25 and c=12

2. Calculate the product a*c by multiplying 12×12=144

3. Find two numbers that multiply to 144 and add to the middle coefficient b=−25 These numbers are −16 and −9

4. Rewrite the middle term −25*x using the two numbers found:

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 (3*x−4)

(4*x−3)*(3*x−4)

Final Answer

12*x2−25*x+12=(4*x−3)*(3*x−4)

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