Factor 6x^2-17x+12

Problem

6*x2−17*x+12

Solution

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

2. Calculate the product a*c which is 6×12=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

6*x2−8*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.

2*x*(3*x−4)−3*(3*x−4)

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

(3*x−4)*(2*x−3)

Final Answer

6*x2−17*x+12=(3*x−4)*(2*x−3)

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