Factor x^2-22x+121

Problem

x2−22*x+121

Solution

1. Identify the structure of the quadratic expression a*x2+b*x+c where a=1 b=−22 and c=121

2. Recognize that the first term x2 is a perfect square of x and the last term 121 is a perfect square of 11

3. Check if the middle term fits the pattern for a perfect square trinomial a2−2*a*b+b2 which factors into (a−b)2

4. Verify the middle term by calculating 2⋅x⋅11=22*x Since the middle term is −22*x the expression matches the pattern (x−11)2

Final Answer

x2−22*x+121=(x−11)2

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