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If f(x)=|(1,x,x+1),(2x, x(x-1(, x(x+1)),...

If `f(x)=|(1,x,x+1),(2x, x(x-1(, x(x+1)),(3x(x-1), x(x-1)(x-2), x(x-1)(x+1))|` then (A) `f(x)` is a polynomial of degree 4 (B) `f(x)` is an odd function (C) `f(x)` is a costant function (D) `f(x)` is an even function

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