When is $x^2 +1$ a factor of $(3+x^4)^n-(x^2+3)^n(x^2-1)^n$?

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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

1. all \(n\);

2. even \(n\);

3. odd \(n\);

4. \(n \geq 3\);

5. 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?