Factor x^2+5

Problem

x2+5

Solution

1. Identify the expression as a sum of squares in the form a2+b2

2. Apply the formula for factoring a sum of squares over the complex numbers, which is a2+b2=(a+b*i)*(a−b*i)

3. Determine the values of a and b by taking the square roots of the terms. Here, a=√(,x2)=x and b=√(,5)

4. Substitute these values into the complex factoring pattern to obtain the final factors.

Final Answer

x2+5=(x+i√(,5))*(x−i√(,5))

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