Factor 6x^2-11x+4

Problem

6*x2−11*x+4

Solution

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

2. Find two numbers that multiply to a⋅c=6⋅4=24 and add to b=−11

3. Determine the pair of numbers, which are −8 and −3 since (−8)*(−3)=24 and −8+(−3)=−11

4. Rewrite the middle term −11*x using the two numbers found: 6*x2−8*x−3*x+4

5. Factor by grouping the first two terms and the last two terms: (6*x2−8*x)+(−3*x+4)

6. Factor out the greatest common factor from each group: 2*x*(3*x−4)−1*(3*x−4)

7. Factor out the common binomial (3*x−4) to obtain the final factored form.

Final Answer

6*x2−11*x+4=(2*x−1)*(3*x−4)

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