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The Real Donald Trump PNG That Everyone’s Hashtagting – Can You Guess Why? - Sterling Industries

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Let $ u = x^2 + 1 \Rightarrow x^2 = u - 1 $, so:
x^4 = (x^2)^2 = (u - 1)^2 = u^2 - 2u + 1
x^4 + 2x^2 + 2 = (u^2 - 2u + 1) + 2(u - 1) + 2
u^2 - 2u + 1 + 2u - 2 + 2 = u^2 + 1
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**:

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