下列哪個多項式可被因式分解?(提示:先因式分解x6-1)
A.x2+x+1
B.x2-x+1
C.x4+x2+1
D.x4-x2+1
maths~~~~
2009-11-29 9:06 pm
回答 (1)
2009-11-29 9:17 pm
✔ 最佳答案
x^6 - 1 = (x^2)^3 - 1
= (x^2 - 1) (x^4 + x^2 + 1).....(1)
又
x^6 - 1
= (x^3)^2 - 1
= (x^3 - 1)(x^3 + 1)
= (x - 1)(x^2 + x + 1)(x+1)(x^2 - x + 1)
= (x^2 - 1) (x^2 + x + 1)(x^2 - x + 1).....(2)
(1) = (2) :
(x^2 - 1)(x^4 + x^2 + 1) = (x^2 - 1)(x^2 + x + 1)(x^2 - x - 1)
x^4 + x^2 + 1 = (x^2 + x + 1)(x^2 - x + 1)
Answer : C
收錄日期: 2021-04-21 22:04:58
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091129000051KK00631