Final answer:
Eukaryotes are the type of microorganisms that possess a membrane-bound nucleus and membrane-bound organelles and undergo mitotic cell division.
Step-by-step explanation:
The type of microorganism that possesses a membrane-bound nucleus and membrane-bound organelles, and undergoes mitotic cell division is Eukaryote.
Eukaryotes are organisms that include protozoans, algae, fungi, plants, and animals. They have a complex nuclear membrane surrounding their nucleus and membrane-bound organelles in the cytoplasm. Eukaryotes are the type of microorganisms that possess a membrane-bound nucleus and membrane-bound organelles and undergo mitotic cell division.
In contrast, bacteria (option A) and archaea (option B) are prokaryotes, which lack a membrane-bound nucleus and membrane-bound organelles. Viruses (option D) are not considered to be living organisms as they require a host to replicate and do not have a membrane-bound nucleus or organelles.