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Home » Where to Watch THE Masters—Don’t Miss This Epic Prize-Packed Show! - 500apps

Where to Watch THE Masters—Don’t Miss This Epic Prize-Packed Show! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Find the remainder when \( u^4 + 3 \) is divided by \( u^2 - 2u + 2 \).

📌 We are to divide \( u^4 + 3 \) by \( u^2 - 2u + 2 \) and find the remainder. Since the divisor is quadratic, the remainder must be linear or constant: let \( R(u) = au + b \).

📌 u^4 + 3 = (u^2 - 2u + 2)Q(u) + au + b

📌 To find \( a \) and \( b \), perform polynomial division or use substitution with roots of the divisor.

📌 Letâs use the roots of \( u^2 - 2u + 2 = 0 \). The discriminant is \( 4 - 8 = -4 \), so roots are:

📌 u = rac{2 \pm \sqrt{-4}}{2} = rac{2 \pm 2i}{2} = 1 \pm i

📌 Let \( lpha = 1 + i \), \( eta = 1 - i \). Then at \( u = lpha \):

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