Okay, let's tackle this question. The patient has a family history of colon cancer—his father died at 45, and his cousin had multiple polyps leading to colectomy. The key here is the family history suggesting a hereditary condition. The options probably include mutations like APC, MLH1, MSH2, etc.

The cousin's multiple polyps and young age point to familial adenomatous polyposis (FAP), which is caused by mutations in the APC gene. FAP typically presents with hundreds to thousands of polyps in the colon, leading to cancer if untreated. Since the patient's cousin has this, the family is likely affected by APC mutations.

Other possibilities like Lynch syndrome (HNPCC) involve mismatch repair genes like MLH1 or MSH2. But Lynch is more about right-sided colon cancers, later in life, and associated with other cancers like endometrial. However, the cousin's multiple polyps and total colectomy are classic for FAP.

So the correct answer should be APC gene mutation. Let me check the options again. If the options include APC, that's the answer. The other options like BRCA, TP53, or others are for different cancers. The patient's family history and cousin's condition strongly indicate APC.

**Core Concept**
This question tests knowledge of hereditary colorectal cancer syndromes. Familial adenomatous polyposis (FAP) is an autosomal dominant condition caused by germline mutations in the **APC gene**, leading to hundreds of colonic adenomas and near-100% lifetime risk of colorectal cancer if untreated. The clinical presentation includes early-onset polyps and a strong family history.

**Why the Correct Answer is Right**
The patient’s cousin has multiple colonic polyps and underwent total colectomy, which is classic for **FAP**. The APC gene encodes a tumor suppressor protein critical for regulating cell proliferation and β-catenin signaling. Germline APC mutations cause uncontrolled β-catenin activation, driving polyp formation. Given the family history, this patient is at high risk for inheriting an APC mutation. Genetic testing for APC is the most appropriate next step.

**Why Each Wrong Option is Incorrect**
**Option A:** BRCA1/BRCA2 mutations are linked to breast/ovarian cancer, not colorectal.
**Option B:** MLH1/MSH2 mutations cause Lynch syndrome (hereditary nonpolyposis CRC), characterized by fewer polyps and later-onset cancer, not the polyposis described.
**Option C:** TP53 mutations are associated with Li-Fraumeni syndrome, which increases risks of sarcomas, breast cancer, and brain tumors, not colonic polyposis.

**Clinical Pearl / High-Yield Fact**
**FAP vs. Lynch syndrome**: Remember “**Polyps = Polyposis**” (FAP) and “**Fewer = HNPCC**” (Lynch). FAP presents with **hundreds of polyps** and colectomy is curative; Lynch has **fewer polyps** and higher risk of extracolonic cancers. Genetic testing is critical for family members.

**Correct Answer: C. APC gene mutation**

✓ Correct Answer: C. APC