Factor 4x^2-11x+6

Problem

4*x2−11*x+6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=−11 and c=6

2. Calculate the product a*c which is 4⋅6=24

3. Find two numbers that multiply to 24 and add to the middle coefficient b=−11 These numbers are −8 and −3

4. Rewrite the middle term −11*x using the two numbers found: −8*x−3*x

4*x2−8*x−3*x+6

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

4*x*(x−2)−3*(x−2)

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

(4*x−3)*(x−2)

Final Answer

4*x2−11*x+6=(4*x−3)*(x−2)

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