Review question

# When is $(1-x)^n (2-x)^{2n} (3-x)^{3n} (4-x)^{4n} (5-x)^{5n}$ negative? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6674

## Suggestion

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?