# 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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