Factor x^(2) + 64

Question

Factor
`x^(2)` + 64

Answer 1

`x^(2) + 64` can be factored into
`(x + 8i)(x - 8i)`, where
`i` is the imaginary unit.

Answer 2

The expression x^2 + 64 is a quadratic expression that cannot be factored using real numbers. However, it can be factored using complex numbers.

We know that i^2 = -1, so we can write:

x^2 + 64 = x^2 - (-64)

Now, we can use the difference of squares formula, which states that:

a^2 - b^2 = (a + b)(a - b)

Using this formula, we can write:

x^2 + 64 = (x + 8i)(x - 8i)

Therefore, the factored form of x^2 + 64 is (x + 8i)(x - 8i).