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📅 May 1, 2026 👤 scraface

May 01, 2026

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But we are given four values, so we reconstruct $ p(x) $.
Let $ p(x) = ax^3 + bx^2 + cx + d $
Use the values:
$ p(0) = d = 2 $
$ p(1) = a + b + c + d = 5 \Rightarrow a + b + c = 3 $
$ p(2) = 8a + 4b + 2c + d = 12 \Rightarrow 8a + 4b + 2c = 10 $
$ p(3) = 27a + 9b + 3c + d = 31 \Rightarrow 27a + 9b + 3c = 29 $
From (2): $ a + b + c = 3 $
Multiply by 2: $ 2a + 2b + 2c = 6 $
Subtract from (3):

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