Factor 2x^2-12x+18

Problem

2*x2−12*x+18

Solution

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

2*(x2−6*x+9)

2. Identify the quadratic pattern inside the parentheses, noting that it is a perfect square trinomial of the form a2−2*a*b+b2

x2−2*(3)*(x)+3

3. Apply the perfect square formula (a−b)2=a2−2*a*b+b2 where a=x and b=3

2*(x−3)2

Final Answer

2*x2−12*x+18=2*(x−3)2

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