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Home » \[ y - (-3) = 3(x - 2) \] - Simpleprint

\[ y - (-3) = 3(x - 2) \] - Simpleprint

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Since \( p(1) = 0 \), \( x = 1 \) is indeed a root. To check the multiplicity, we compute the derivative \( p'(x) \):

📌 p'(x) = 4x^3 - 12x^2 + 12x - 4

📌 Now, evaluate \( p'(1) \):

📌 p'(1) = 4 imes 1^3 - 12 imes 1^2 + 12 imes 1 - 4 = 4 - 12 + 12 - 4 = 0

📌 Since \( p'(1) = 0 \), \( x = 1 \) is a root of multiplicity at least 2. Compute the second derivative \( p''(x) \):

📌 p''(x) = 12x^2 - 24x + 12

📌 Evaluate \( p''(1) \):

📌 p''(1) = 12 imes 1^2 - 24 imes 1 + 12 = 12 - 24 + 12 = 0

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