polynomial

2012-04-22 11:41 pm
If a polynomial Q(X) is divisible by X + 1, then Q(X) must be divisible by X. 點解呢 ?

回答 (1)

2012-04-23 12:44 am
✔ 最佳答案
你會唔會出錯題呢?
應該係Q(x-1) must be divisible by x
or ???

若如我如上估計的問題,則其解如下:

Q(x) divisible by x + 1
according to remainder thm,
Q(-1) = 0
Let g(x) = Q(x-1)
If g(x) divided by x
According to remainder thm
the remainder will be:
g(0)
to switch back to function Q
g(0) = Q(0-1) = Q(-1)
where Q(-1) = 0 which is given
Therefore Q(x-1) is divisible by x

參考: 經數學人 ronaldchik.blogspot.com


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