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To find the remainder when \( t^4 + 3t^2 + 2 \) is divided by \( t^2 + 1 \), we use polynomial long division or the remainder theorem. We express \( t^4 + 3t^2 + 2 \) in the form:
t^4 + 3t^2 + 2 = (t^2 + 1)Q(t) + R(t)
where \( R(t) \) is the remainder and has degree less than 2. Assume \( R(t) = at + b \).

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