Factor 2x^2-4x+2

Problem

2*x^2−4*x+2

Solution

1. Identify the greatest common factor (GCF) for all terms in the expression.

2. Factor out the GCF, which is 2 from the expression.

2*(x^2−2*x+1)

3. Recognize the quadratic expression inside the parentheses as a perfect square trinomial of the form a^2−2*a*b+b^2=(a−b)^2

4. Factor the trinomial x^2−2*x+1 into (x−1)^2

2*(x−1)^2

Final Answer

2*x^2−4*x+2=2*(x−1)^2

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