Factor 6x^2-13x+6

Problem

6*x2−13*x+6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=−13 and c=6

2. Calculate the product a*c which is 6⋅6=36

3. Find two numbers that multiply to 36 and add to the middle coefficient b=−13 These numbers are −9 and −4

4. Rewrite the middle term −13*x using the two numbers found: −9*x−4*x

6*x2−9*x−4*x+6

5. Factor by grouping the first two terms and the last two terms.

3*x*(2*x−3)−2*(2*x−3)

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

(3*x−2)*(2*x−3)

Final Answer

6*x2−13*x+6=(3*x−2)*(2*x−3)

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