Remainder Thm

👨🏻‍🏫 學術台數學

[匿名]

2013-08-01 5:39 am

Find the remainder when x^20 + 1 is divided by x^2 - 2x + 1.

回答 (2)

myisland8132

2013-08-01 7:28 am

✔ 最佳答案

Let x^20 + 1 = Q(x)(x^2 - 2x + 1) + Ax + B

Sub. x = 1

A + B = 2

Diffentiate both sides r.s.t x

20x^19 = Q(x)(2x - 2) + (x^2 - 2x + 1)Q'(x) + A

Sub. x = 1 => A = 20

So, B = -18

The remainder is 20x - 18

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知足常樂

2013-08-01 7:38 am

Please read my full solution as below:

圖片參考：http://imgcld.yimg.com/8/n/HA00430218/o/20130731233748.jpg

參考: Calculated

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收錄日期: 2021-04-27 19:21:42
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