Factor 2x^2-8x+8

Problem

2*x^2−8*x+8

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^2−4*x+4)

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. Identify the components where a=x and b=2 since x^2=(x)^2 4=(2)^2 and 4*x=2*(x)*(2)

5. Factor the trinomial into its squared binomial form.

2*(x−2)^2

Final Answer

2*x^2−8*x+8=2*(x−2)^2

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