Final answer:
Erythropoiesis is the term used for the process of synthesizing new red blood cells in the red bone marrow, part of the broader hematopoiesis process.
Step-by-step explanation:
The term that describes the process of synthesizing new red blood cells within the red bone marrow is B) Erythropoiesis. Hematopoiesis is the broader process in which all blood cells, including red blood cells, white blood cells, and platelets, are produced by the red bone marrow. Erythropoiesis is specifically the production of red blood cells. This synthesis is regulated by hemopoietic growth factors, such as erythropoietin, which promote the differentiation and proliferation of the erythrocyte lineage.