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

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

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

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

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?