Factor 12x^2-17x+6

Problem

12*x2−17*x+6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=12 b=−17 and c=6

2. Calculate the product a*c by multiplying 12×6=72

3. Find two numbers that multiply to 72 and add to the middle coefficient b=−17 These numbers are −8 and −9

4. Rewrite the middle term −17*x using the two numbers found: −8*x−9*x

12*x2−8*x−9*x+6

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−2)−3*(3*x−2)

6. Factor out the common binomial (3*x−2)

(4*x−3)*(3*x−2)

Final Answer

12*x2−17*x+6=(4*x−3)*(3*x−2)

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