Factor x^2+121

Problem

x^2+121

Solution

1. Identify the expression as a sum of two squares, which follows the form a^2+b^2

2. Recognize that 121 is a perfect square, specifically 11^2

3. Apply the formula for factoring a sum of squares over the complex numbers, which is a^2+b^2=(a+b*i)*(a−b*i)

4. Substitute a=x and b=11 into the complex factoring formula.

Final Answer

x^2+121=(x+11*i)*(x−11*i)

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