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Vector from point on line to \(\mathbfp\): - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Find the remainder when $ t^3 + 2t^2 - 5t + 6 $ is divided by $ t - 1 $.

📌 We are asked to find the remainder when

📌 f(t) = t^3 + 2t^2 - 5t + 6

📌 is divided by $ t - 1 $.

📌 By the **Remainder Theorem**, the remainder is simply $ f(1) $.

📌 f(1) = 1^3 + 2(1)^2 - 5(1) + 6 = 1 + 2 - 5 + 6 = 4.

📌 So the remainder is:

📌 f(x + 1) - f(x) = 6x + 4.

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