Let \(n\) be a positive integer. Then \(x^2 +1\) is a factor of

\[(3+x^4)^n-(x^2+3)^n(x^2-1)^n\]

for

all \(n\);

even \(n\);

odd \(n\);

\(n \geq 3\);

- no values of \(n\).

What ideas can we use if we know \(x^2+1\) is a factor?

What is the same and what is different about this question compared to other polynomial factorisation questions?