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)*(x+1)

5. Simplify the expression by writing the repeated factors as a square.

2*(x+1)^2

Final Answer

2*x^2+4*x+2=2*(x+1)^2

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