**Core Concept**
The process of phagocytosis involves the engulfment and destruction of foreign particles, such as bacteria, by specialized cells of the immune system. In the context of blood smears, the cell type responsible for phagocytosing bacteria is a type of white blood cell.

**Why the Correct Answer is Right**
The correct answer is a type of granulocyte, which is a subtype of white blood cells that contains granules filled with enzymes and antimicrobial peptides. These granules enable the cell to phagocytose and kill bacteria. Specifically, the cell type responsible for phagocytosing bacteria at sites of infection is the neutrophil, which is the most abundant type of granulocyte in blood smears. Neutrophils contain azurophilic and specific granules that contain enzymes such as myeloperoxidase and defensins, which help to kill ingested bacteria.

**Why Each Wrong Option is Incorrect**
* **Option A:** Lymphocytes are a type of white blood cell involved in adaptive immunity, but they are not primarily responsible for phagocytosing bacteria. Lymphocytes can activate and coordinate the immune response, but they do not contain granules or enzymes to phagocytose and kill bacteria.
* **Option B:** Monocytes are a type of white blood cell that circulates in the blood and matures into macrophages in tissues. While macrophages are capable of phagocytosing bacteria, monocytes are not typically involved in this process in blood smears.
* **Option C:** Eosinophils are a type of granulocyte, but they are primarily involved in combating parasitic infections and in allergic reactions. Eosinophils contain granules that contain major basic protein, which helps to kill parasites and eosinophils are not typically involved in phagocytosing bacteria.

**Clinical Pearl / High-Yield Fact**
In blood smears, the presence of a high number of neutrophils can indicate an acute bacterial infection, such as pneumonia or sepsis. Conversely, a low number of neutrophils can indicate a chronic infection or a compromised immune system.

**Correct Answer: C. Neutrophils**