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A factored polynomial reveals its roots, a key concept in understanding the behavior of these expressions.

Using the identity \( a^3 - b^3 = ( a -b ) ( a^2 + ab + b^2 ) \), which of the following must be a factor of

\[ x^3 + 8 ? \]

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Using the identity \( a^2 - b^2 = (a-b) ( a+b) \), which of the following must be a factor of

\[ x^4 + 2500 ? \]

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**non-positive integers** such that the following is an algebraic identity in \(x\): \[(x-a)^2(x+a)^2=x^4+bx^3+cx^2+dx+256.\] What is the value of \(-a-b-c-d\)?

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Which of the following is a factor of \(x^4 - 81\)?

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