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Home » Subtract 36: \( b^2 = 64 \). - RedTag Digital

Subtract 36: \( b^2 = 64 \). - RedTag Digital

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 $ 12a + 2b = 8 $ → $ 6a + b = 4 $

📌 $ 18a + 2b = 16 $ → $ 9a + b = 8 $

📌 Subtracting these gives $ 3a = 4 $ → $ a = \frac{4}{3} $. Substituting back, $ b = -4 $. Then, from $ 7a + 3b + c = 7 $, we find $ c = \frac{35}{3} $. Finally, $ d = -6 $. Thus,

📌 g(x) = \frac{4}{3}x^3 - 4x^2 + \frac{35}{3}x - 6.

📌 The final answer is $ \boxed{\dfrac{4}{3}x^3 - 4x^2 + \dfrac{35}{3}x - 6} $.

📌 Question: An epidemiologist models the spread of a disease with the polynomial $ g(x) $, where $ g(x^2 - 1) = 2x^4 - 5x^2 + 1 $. Find $ g(x^2 + 1) $.

📌 Solution: Let $ y = x^2 - 1 $. Then $ x^2 = y + 1 $. Substitute into $ g(y) = 2x^4 - 5x^2 + 1 $:

📌 x^4 = (x^2)^2 = (y + 1)^2 = y^2 + 2y + 1.

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