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Step-by-Step Solution
Key Concept: Use row operations R1 -> R1 + R2 + R3 to factor out (x+4) and then simplify the determinant.
Applying R1 -> R1 + R2 + R3, the determinant becomes (x+4) times a determinant with 1s in the first row. Further row operations C2 -> C2 - C1 and C3 -> C3 - C1 lead to (x+4)(x-4)^2. Comparing with (A+Bx)(x-A)^2, we get A=-4 and B=5.
Correct Answer: 2