Factor 6x^2-5x+1

Problem

6*x2−5*x+1

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=−5 and c=1

2. Find two numbers that multiply to a⋅c=6 and add to b=−5

3. Determine the pair of numbers, which are −2 and −3 since (−2)*(−3)=6 and −2+(−3)=−5

4. Rewrite the middle term −5*x using the two numbers found.

6*x2−2*x−3*x+1

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

2*x*(3*x−1)−1*(3*x−1)

6. Factor out the common binomial factor (3*x−1)

(2*x−1)*(3*x−1)

Final Answer

6*x2−5*x+1=(2*x−1)*(3*x−1)

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