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Step-by-Step Solution
Key Concept: Use row operations R1 -> R1 + R2 + R3 to factor out (5x-4) and then simplify the determinant to find the form (A+Bx)(x-A)^2.
Adding R1 -> R1 + R2 + R3 gives the first row as (5x-4, 5x-4, 5x-4). Factoring out (5x-4) and performing column operations C2 -> C2 - C1 and C3 -> C3 - C1 leads to (5x-4) * |1 0 0; 2x x-4-2x 0; 2x 0 x-4-2x| = (5x-4) * (-x-4)^2 = (5x-4)(x+4)^2. Comparing with (A+Bx)(x-A)^2, we get A=-4 and B=5.
Correct Answer: 2