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📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Find the cubic polynomial \( f(x) \) such that \( f(1) = 3 \), \( f(2) = -1 \), \( f(3) = 2 \), and \( f(4) = 5 \).

📌 To find the cubic polynomial \( f(x) = ax^3 + bx^2 + cx + d \), we use the given conditions to set up a system of equations:

📌 \( f(1) = a(1)^3 + b(1)^2 + c(1) + d = 3 \), which simplifies to:

📌 a + b + c + d = 3

📌 \( f(2) = a(2)^3 + b(2)^2 + c(2) + d = -1 \), which simplifies to:

📌 8a + 4b + 2c + d = -1

📌 \( f(3) = a(3)^3 + b(3)^2 + c(3) + d = 2 \), which simplifies to:

📌 27a + 9b + 3c + d = 2

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