Find the Remainder Of $p ( x ) = 22 x ^ { 2004 } - 5 x ^ { 569 } + x ^ { 104 } - 27 x + 22 x ^ { 2003 } - 5 x ^ { 568 } + x ^ { 103 } - 27$

question 96

Essay

Find the remainder of $p ( x ) = 22 x ^ { 2004 } - 5 x ^ { 569 } + x ^ { 104 } - 27 x + 22 x ^ { 2003 } - 5 x ^ { 568 } + x ^ { 103 } - 27$ , if $p ( x )$ is divided by $( x + 1 )$ . What is the significance of this remainder?

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Definitions:

Independently

Acting on one's own; making decisions or taking action based on one's own judgment without relying on others.

Commons Dilemma

A situation in which individuals' short-term selfish interests are at odds with long-term group benefits, leading to the overuse or depletion of common resources.

Accountable

Being responsible or answerable for one's actions or the execution of duties, often involving a level of transparency.

Transactive Memory

A shared system of remembering information among members of a group, allowing the group to store, encode, and retrieve information more effectively than individual members working alone.