Evaluate using partial fractions
x^4 - 16/x^3 - 8
did you mean (x^4 - 16)/(x^3 - 8) ? , then
= (x+2)(x-2)/((x-2)(x^2 + 2x + 4))
= (x+2)/(x^2 + 2x + 4) , x ≠ 2
In the process of partial fractions, the denominator usually factors into rational factors.
Your denominator does not factor.
So unless we use complex number factors, this does not fit into the category of "partial fractions"