Factor the expression over the complex numbers. x^2+36

1 answer:

5 0

Note that
a² - b² = (a+b)(a-b)
i² = -1 by definition.

We want to factorize x² + 36 = x² + 6².

Consider the expression
x² - (6i)² = x² - (6²)(i²) = x² - 36i² = x² + 36

Because x² - (6i)² = (x + 6i)(x - 6i)
Therefore
x² + 36 = (x + 6i)(x - 6i)

Answer: (x + 6i)(x - 6i)

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