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Home » Set equal to $ 2t + 1 $: - Roya Kabuki

Set equal to $ 2t + 1 $: - Roya Kabuki

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 Check with \( x = 2 \): \( y = 3 \cdot 2^2 = 12 \), which matches.

📌 So \( a = 3 \).

📌 What is the remainder when \( x^4 - 3x^2 + 2x + 5 \) is divided by \( x - 1 \)?

📌 Use Remainder Theorem: evaluate at \( x = 1 \).

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

📌 \( x^2 + (x+1)^2 = 145 \) → \( x^2 + x^2 + 2x + 1 = 145 \) → \( 2x^2 + 2x - 144 = 0 \).

📌 Divide by 2: \( x^2 + x - 72 = 0 \) → \( (x + 9)(x - 8) = 0 \).

📌 So \( x = 8 \), larger integer is 9.

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