Factor 2x^2-3x+1

Problem

2*x2−3*x+1

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−3 and c=1

2. Find two numbers that multiply to a⋅c=2⋅1=2 and add to b=−3

3. Determine the pair of numbers, which are −2 and −1 since (−2)⋅(−1)=2 and (−2)+(−1)=−3

4. Rewrite the middle term −3*x using the two numbers found: 2*x2−2*x−x+1

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

6. Factor out the common binomial (x−1) to obtain the final factored form.

Final Answer

2*x2−3*x+1=(2*x−1)*(x−1)

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