Factor x^2+16

Problem

x2+16

Solution

1. Identify the expression as a sum of squares in the form a2+b2 where a=x and b=4

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

4. Simplify the resulting binomial factors.

Final Answer

x2+16=(x+4*i)*(x−4*i)

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