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Home » Breaking Boundaries: Age Ice 2 Is Here—Are You Ready? - AIKO, infinite ways to autonomy.

Breaking Boundaries: Age Ice 2 Is Here—Are You Ready? - AIKO, infinite ways to autonomy.

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 f(x) = -\frac{14}{3}x^3 + 33x^2 - \frac{211}{3}x + 45

📌 Now compute $ f(5) $:

📌 f(5) = -\frac{14}{3}(125) + 33(25) - \frac{211}{3}(5) + 45 = -\frac{1750}{3} + 825 - \frac{1055}{3} + 45

📌 = \left(-\frac{1750 + 1055}{3}\right) + (825 + 45) = -\frac{2805}{3} + 870 = -935 + 870 = -65

📌 Thus, $ f(5) = \boxed{-65} $

📌 Question: An anthropologist models cultural adaptation index $ A(x) $ over time $ x $ (in decades) using a cubic polynomial satisfying $ A(1) = 2 $, $ A(2) = -4 $, $ A(3) = 6 $, and $ A(4) = -8 $. Find the remainder when $ A(x)^3 + 2 $ is divided by $ x - 5 $.

📌 Solution: By the Remainder Theorem, the remainder when $ A(x)^3 + 2 $ is divided by $ x - 5 $ is $ A(5)^3 + 2 $. So we must compute $ A(5) $.

📌 Let $ A(x) = ax^3 + bx^2 + cx + d $. Use the given values:

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