SOLUTION: find the remainder when p(x)=x10-3 is divided by x2-1（10 and 2 are both powers of x）

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Question 1169561: find the remainder when p(x)=x10-3 is divided by x2-1（10 and 2 are both powers of x）
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Write the given polynomial in the form


    p(x) = x%5E10-3 = (%28%28x%5E2%29%5E5-1%29%29 - 2.


The polynomial  %28x%5E2%29%5E5-1%29 is divisible by (x^2-1) with no remainder, which  is ONVIOUS (= or is a well known fact).


Therefore, the remainder under the problem's question is -2.     ANSWER

Solved.