Here's why:

* Neutrophils are a type of white blood cell, which are essential components of the human immune system.

* White blood cells are found in animals, which are all eukaryotic organisms.

* Prokaryotes are single-celled organisms without a nucleus or other membrane-bound organelles. Examples include bacteria and archaea.

* Eukaryotes have a nucleus and other membrane-bound organelles. Examples include plants, animals, fungi, and protists.

Since neutrophils are complex cells with a nucleus and other organelles, they are classified as eukaryotic.