Polynomial Coeficients

Algebra Level 5

\[ \large P(x)=A{ x }^{ 7 }+B{ x }^{ 6 }+C{ x }^{ 5 }+D{ x }^{ 4 }+E{ x }^{ 3 }+F{ x }^{ 2 }+G{ x }^{ 1 }+H \]

Let \(P(x) \) be a \(7^\text{th} \) degree polynomial such that \( P(x) + 1 \) is divisible by \( { (x-1) }^{ 4 } \) and \( P(x) - 1 \) is divisible by \( { (x+1) }^{ 4 } \). Evaluate \( C+E \).

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