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Home » Distance: \(30t + 5(4 - t) = 120\). - DNSFLEX

Distance: \(30t + 5(4 - t) = 120\). - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Substitute into (6):

📌 12a + 3(2 - 3a) = 10 \Rightarrow 12a + 6 - 9a = 10 \Rightarrow 3a = 4 \Rightarrow a = \frac{4}{3}

📌 Then $ b = 2 - 3 \cdot \frac{4}{3} = 2 - 4 = -2 $

📌 From (2): $ \frac{4}{3} - 2 + c = 3 \Rightarrow c = 3 + 2 - \frac{4}{3} = 5 - \frac{4}{3} = \frac{11}{3} $

📌 And $ d = 2 $

📌 p(x) = \frac{4}{3}x^3 - 2x^2 + \frac{11}{3}x + 2

📌 Thus, the remainder when $ p(x) $ is divided by $ x^4 - 1 $ is simply $ p(x) $, since $ \deg p < 4 $. So the remainder is:

📌 \boxed{\frac{4}{3}x^3 - 2x^2 + \frac{11}{3}x + 2}

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