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Home » Level 2: 1.2 × 1.2 = 1.44 - AMAZONAWS

Level 2: 1.2 × 1.2 = 1.44 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Wait: actually, **any** polynomial $ p(x) $ of degree less than 4 **is** the remainder upon division by $ x^4 - 1 $. Since $ \deg(p) = 3 < 4 $, the division algorithm gives:

📌 p(x) = 0 \cdot (x^4 - 1) + p(x)

📌 So the remainder is **$ p(x) $** itself. But the problem asks for the remainder — which is a polynomial of degree less than 4 — so it is $ p(x) $, but we are to **report it in standard form**.

📌 But we are given four values, so we reconstruct $ p(x) $.

📌 Let $ p(x) = ax^3 + bx^2 + cx + d $

📌 Use the values:

📌 $ p(0) = d = 2 $

📌 $ p(1) = a + b + c + d = 5 \Rightarrow a + b + c = 3 $

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