Factor 3x^2-6x+3

Problem

3*x2−6*x+3

Solution

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

2. Factor out the common constant 3 from the quadratic expression.

3*(x2−2*x+1)

3. Recognize the expression inside the parentheses as a perfect square trinomial of the form a2−2*a*b+b2=(a−b)2

4. Factor the quadratic trinomial x2−2*x+1 into its squared binomial form.

(x−1)2

5. Combine the constant factor and the squared binomial to reach the final factored form.

Final Answer

3*x2−6*x+3=3*(x−1)2

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