Find the Real Zeros of the Polynomial Function $f ( x ) = x ^ { 5 } - 16 x ^ { 4 } + 64 x ^ { 3 }$

Multiple Choice

Find the real zeros of the polynomial function $f ( x ) = x ^ { 5 } - 16 x ^ { 4 } + 64 x ^ { 3 }$ and determine the multiplicity of each.

A) $x = 0$ , multiplicity 2; $x = 8$ , multiplicity 3
B) $x = 0$ , multiplicity 2; $x = 8$ , multiplicity 1; $x = - 8$ , multiplicity 2
C) $x = 0$ , multiplicity 3; $x = 8$ , multiplicity 2
D) $x = 0$ , multiplicity 3; $x = - 8$ , multiplicity 2
E) $x = 0$ , multiplicity 2; $x = 8$ , multiplicity 2; $x = - 8$ , multiplicity 1