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📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 f(2) = (2)^2 - 4(2) + m = 4 - 8 + m = -4 + m.

📌 + 3m = -4 + m \implies 2m = 0 \implies m = 0.

📌 Question: A linguist analyzes the frequency of a linguistic pattern with $ h(x) = x^2 - 2x + m $. If the frequency at $ x = 5 $ is 12, determine $ m $.

📌 Solution: Substitute $ x = 5 $ into $ h(x) $:

📌 h(5) = (5)^2 - 2(5) + m = 25 - 10 + m = 15 + m.

📌 Set this equal to 12:

📌 + m = 12 \implies m = -3.

📌 Question: Expand the product $ (x^2 - 3x + 2m)(x^2 - 3x + 5m) $ and simplify.

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