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anniversary gifts for him - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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Now, substitute $ x^2 - 1 $ into $ g $:
g(x^2 - 1) = (x^2 - 1)^2 + 1 = x^4 - 2x^2 + 1 + 1 = x^4 - 2x^2 + 2
Thus, the answer is:
\boxed{x^4 - 2x^2 + 2}
Question: Find the remainder when $ u^3 + 2 $ is divided by $ u + 1 $.
We use the **Remainder Theorem**:
The remainder when a polynomial $ f(u) $ is divided by $ u - c $ is $...
Here, divide $ f(u) = u^3 + 2 $ by $ u + 1 = u - (-1) $.
So, compute $ f(-1) $:
f(-1) = (-1)^3 + 2 = -1 + 2 = 1

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