Factor 3x^2-11x+6

Problem

3*x2−11*x+6

Solution

1. Identify the coefficients a b and c from the quadratic expression a*x2+b*x+c where a=3 b=−11 and c=6

2. Calculate the product a*c to find two numbers that multiply to a*c and add to b

a*c=3⋅6=18

3. Find two integers that multiply to 18 and add to −11 These numbers are −9 and −2

4. Rewrite the middle term −11*x using the two integers found.

3*x2−9*x−2*x+6

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

3*x*(x−3)−2*(x−3)

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

(3*x−2)*(x−3)

Final Answer

3*x2−11*x+6=(3*x−2)*(x−3)

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