Factor 2x^2-12x+18

Problem

2*x^2−12*x+18

Solution

1. Factor out the greatest common factor by identifying that each term is divisible by 2

2*(x^2−6*x+9)

2. Identify the quadratic pattern inside the parentheses, noting that it is a perfect square trinomial of the form a^2−2*a*b+b^2

x^2−2*(3)*(x)+3^2

3. Apply the perfect square formula (a−b)^2=a^2−2*a*b+b^2 where a=x and b=3

2*(x−3)^2

Final Answer

2*x^2−12*x+18=2*(x−3)^2

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