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Polynomials & Rational Functions

Review question

When is $x^2 +1$ a factor of $(3+x^4)^n-(x^2+3)^n(x^2-1)^n$?
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Ref: R7243

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Question

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 \(n\).