Step 1: A solitary pedunculated rectal polyp causing painless bleeding in a young child, with biopsy showing dilated cystic glands filled with mucin and inflammatory debris in an inflamed lamina propria, is a juvenile (retention) polyp.
Step 2: Juvenile polyps are smooth-surfaced, reddish, pedunculated lesions usually less than 3 cm. They are hamartomatous, most common in children under 5 years, and typically present with rectal bleeding. The sporadic solitary form carries no malignant potential.
Step 3: Why the others are wrong. Villous adenoma and serrated adenoma are dysplastic neoplastic polyps of adults, not young children. Vascular malformation would not show dilated mucin-filled cystic glands.
Ref: Robbins Basic Pathology, 9th edition, pg 592.