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Home » Turn the Page Now—The Page of Wands Reveals Magic You Never Thought Possible! - Leaselab

Turn the Page Now—The Page of Wands Reveals Magic You Never Thought Possible! - Leaselab

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 So \(a\omega + b = 3\omega + 4\), hence \(a = 3\), \(b = 4\).

📌 Similarly, check at \(\omega^2\) (the conjugate root), but since coefficients are real, and we already matched, the remainder is \(3x + 4\).

📌 Verify using algebra:

📌 x^4 + 3x^3 - 2x^2 + x + 5 = (x^2 - x + 1)(x^2 + ax + b) + ax + c

📌 Expand right-hand side:

📌 = x^4 + (a - 1)x^3 + (b - a + 1)x^2 + (-b + a)x + b

📌 Add \(ax + c\):

📌 x^4 + (a - 1)x^3 + (b - a + 1)x^2 + (-b + a + a)x + (b + c) = x^4 + (a - 1)x^3 + (b - a + 1)x^2 + (2a - b)x + (b + c)

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