The denominator \(x^3 - 8\) is a difference of cubes, which can be factored using the formula \(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\). Here, \(a = x\) and \(b = 2\). Therefore, \(x^3 - 8\) can be factored as:
\[
x^3 - 8 = (x - 2)(x^2 + 2x + 4)
\]
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