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Home » El costo total inicialmente es 12 estudiantes * $150 = $1800. - Portal da AcÃºstica

El costo total inicialmente es 12 estudiantes * $150 = $1800. - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 p(x) = \text{remainder of } p(x) \div (x^4 - 1) \quad \text{only if } \deg p < \deg(x^4 - 1)

📌 But $ p(x) $ is cubic, so remainder $ r(x) = p(x) $, but only if $ x^4 - 1 $ divides $ p(x) - r(x) $, which is not true unless $ p(x) $ is degree ≤3 — which it is.

📌 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:

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