本區搜索:
Yahoo!字典
打印

[Core] Polynomials

[隱藏]

Polynomials

求解
New progress in senior mathematics compulsory part book 5 part 1 Ch10. 4  18 LetP(x)=x^(6)+ax^(5)+bx^(4)+cx^(3)+dx^(2)+ex+f.
If f is a prime number, how many distinct linear factors with integral
coefficients can P(x) at most have?



   

TOP

3
Suppose P(x) can be rewritten as
(x+A)(x+B)(x+C)(x+D)(x+E)(x+F)
f = ABCDEF
Since f is prime,
five of the unknowns must be 1 / -1
and one of the unknowns must be f
P(x) = (x+1)^m (x-1)^n (x+f)
where m+n=5 and m, n are non negative integers.
Hence, if m=1, n=4, the number of linear factor of P(x) is the most.
P(x) = (x+1)(x-1)^4 (x+f) [3 linear factors]



TOP

12

want to know too!

[ 本帖最後由 vikoau 於 2019-7-25 05:10 PM 編輯 ]

TOP

重要聲明:小卒資訊論壇 是一個公開的學術交流及分享平台。 論壇內所有檔案及內容 都只可作學術交流之用,絕不能用商業用途。 所有會員均須對自己所發表的言論而引起的法律責任負責(包括上傳檔案或連結), 本壇並不擔保該等資料之準確性及可靠性,且概不會就因有關資料之任何不確或遺漏而引致之任何損失或 損害承擔任何責任(不論是否與侵權行為、訂立契約或其他方面有關 ) 。