When is $(1-x)^n (2-x)^{2n} (3-x)^{3n} (4-x)^{4n} (5-x)^{5n}$ negative?

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If \(x\) and \(n\) are integers then \[(1-x)^n (2-x)^{2n} (3-x)^{3n} (4-x)^{4n} (5-x)^{5n}\] is

1. negative when \(n>5\) and \(x<5\),

2. negative when \(n\) is odd and \(x>5\),

3. negative when \(n\) is a multiple of \(3\) and \(x>5\),

4. negative when \(n\) is even and \(x<5\).

What happens if we try out some values for \(x\) and \(n\)?

Can we find values such that the expression is positive?