Factor x^2+9

Problem

x2+9

Solution

1. Identify the expression as a sum of squares in the form a2+b2 where a=x and b=3

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 x for a and 3 for b into the complex factoring formula.

4. Verify that the expression cannot be factored further using only real numbers, as it has no real roots.

Final Answer

x2+9=(x+3*i)*(x−3*i)

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