Given two zeros of the polynomial function,find the other ze

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/09 10:07:14

Given two zeros of the polynomial function,find the other zeros.
给个例子来说我的疑问吧：
EX：F（X）=X^4+6X^3-4X^2-54X-45;-3,3
最后那两个-3和3便是the two zeros of given.
但是我用3来作综合除法之后就不知道如何FACTOR这个多项式了,
我的进度是——（X-3）（.）
那么在“.”是什么呢?
还有两个例子：F(X)=3X^4-2X^3-12X^2+6X+9
F(X)=X^4+2X^3-14X^2-32X-32
我还不是很懂啊

长除算法（与数的除法类似）
X^3 + 9 X^2 + 23 X + 15
------------------------------------
X - 3 ) X^4 + 6 X^3 - 4 X^2 - 54 X - 45
X^4 - 3 X^3
--------------
9 X^3 - 4 X^2 - 54 X - 45
9 X^3 - 27 X^2
--------------
23 X^2 - 54 X - 45
23 X^2 - 69 X
-------------
15 X - 45
15 X - 45
---------
0
所以
X^4 + 6 X^3 - 4 X^2 - 54 X - 45
= ( X - 3 )( X^3 + 9 X^2 + 23 X + 15 )
X^2 + 6 X + 5
---------------------------
X + 3 ) X^3 + 9 X^2 + 23 X + 15
X^3 + 3 X^2
-------------
6 X^2 + 23 X + 15
6 X^2 + 18 X
------------
5 X + 15
5 X + 15
--------
0
所以
X^3 + 9 X^2 + 23 X + 15
= ( X + 3 )( X^2 + 6 X + 5 )
而
X^2 + 6 X + 5 = ( X + 1 )( X + 5 )
故
X^4 + 6 X^3 - 4 X^2 - 54 X - 45
= ( X - 3 )( X + 3 )( X + 1 )( X + 5 )

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