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Step-by-Step Solution
Key Concept: Evaluate the determinant f(x) by factoring out common terms from rows and columns, then evaluate f(50) and D_5.
The determinant f(x) simplifies to 0 for all x because the rows are linearly dependent. Specifically, the third row is a multiple of the first two rows. Thus f(50) = 0. Calculating D_5 by substituting r=5 into the determinant D_r gives a value of -1. Therefore, f(50) - D_5 = 0 - (-1) = 1.
Correct Answer: B