Factor 6x^2-11x+3

Problem

6*x2−11*x+3

Solution

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

2. Find two numbers that multiply to a⋅c=6⋅3=18 and add to b=−11

3. Determine the pair of numbers, which are −9 and −2 since (−9)⋅(−2)=18 and (−9)+(−2)=−11

4. Rewrite the middle term −11*x using the two numbers found: 6*x2−9*x−2*x+3

5. Factor by grouping the first two terms and the last two terms: 3*x*(2*x−3)−1*(2*x−3)

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

Final Answer

6*x2−11*x+3=(3*x−1)*(2*x−3)

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