Factor x^2+6

Problem

x2+6

Solution

1. Identify the type of expression. The expression x2+6 is a sum of squares because it is in the form a2+b2 where a=x and b=√(,6)

2. Determine the factorability over real numbers. A sum of squares cannot be factored into linear factors using only real numbers.

3. Apply the complex factorization formula. To factor over the complex numbers, use the identity a2+b2=(a+b*i)*(a−b*i)

4. Substitute the values into the formula. Let a=x and b=√(,6)

x2+6=(x+i√(,6))*(x−i√(,6))

Final Answer

x2+6=(x+i√(,6))*(x−i√(,6))

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