If x(x-1)(x-2)(x-3)+1=k^{2}, then which one of the following is a possible expression for k?

Explanation

Rearrange the given terms: (x(x-3))((x-1)(x-2)) + 1 = (x^2-3x)(x^2-3x+2) + 1. Let y = x^2-3x. The expression becomes y(y+2)+1 = y^2+2y+1 = (y+1)^2. Substituting y back, k^2 = (x^2-3x+1)^2, so k = x^2-3x+1.

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