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legion of super-heroes - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📝 Recent Posts

We are to divide \( u^5 - 3u^3 + 2u + 8 \) by \( u^2 - 2u + 1 \). Note...
\[ u^2 - 2u + 1 = (u - 1)^2 \]
Let \( f(u) = u^5 - 3u^3 + 2u + 8 \). Since the divisor is quadratic,...
By the Remainder Theorem for polynomials, we use polynomial division o...
\[ f(u) = (u - 1)^2 Q(u) + au + b \]
\( f(1) = a(1) + b = a + b \)
Differentiate: \( f'(u) = 2(u - 1)Q(u) + (u - 1)^2 Q'(u) + a \), so \(...
Compute \( f(1) \):
\[ f(1) = 1^5 - 3(1)^3 + 2(1) + 8 = 1 - 3 + 2 + 8 = 8 \]
\[ a + b = 8 \quad ext{(1)} \]

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