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Home » DC’s Epic Comeback is Here—Top 5 Upcoming Movies Shaking the Box Office! - Leaselab

DC’s Epic Comeback is Here—Top 5 Upcoming Movies Shaking the Box Office! - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 ---**Question: A volcanologist is analyzing the seismic waves produced by a volcanic eruption. Let \( f(t) \) be a polynomial representing the amplitude of a seismic wave over time \( t \). Find the remainder when \( t^4 + 3t^2 + 2 \) is divided by \( t^2 + 1 \).

📌 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 \( R(t) = at + b \).

📌 Divide the leading term \( t^4 \) by \( t^2 \) to get \( t^2 \).

📌 Multiply \( t^2 \) by \( t^2 + 1 \) to get \( t^4 + t^2 \).

📌 Subtract: \( (t^4 + 3t^2 + 2) - (t^4 + t^2) = 2t^2 + 2 \).

📌 Divide \( 2t^2 \) by \( t^2 \) to get \( 2 \).

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