Factor 2x^2+20x+50

Problem

2*x^2+20*x+50

Solution

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

2*(x^2+10*x+25)

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

x^2+2*(5)*(x)+5^2

3. Apply the perfect square formula (a+b)^2=a^2+2*a*b+b^2 where a=x and b=5

2*(x+5)^2

Final Answer

2*x^2+20*x+50=2*(x+5)^2

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