when a polynomial f(x) is divided by x-4 and 3x-2, the remainders are -5 and 15
respectively. find the remainder when f(x) is divided by (x-4)(3x-2).
要步驟
polynomial2
2010-02-21 6:57 am
回答 (2)
2010-02-21 7:19 am
✔ 最佳答案
依題意f(x)=(x-4)Q1(x)-5f(x)=(3x-2)Q2(x)+15
故可設f(x)=(x-4)(3x-2)Q(x)+k(x-4)-5
由f(2/3)=-5=-10k/3得k=-3/2
所以,所求餘式為-3/2(x-4)-5即-3/2x +1。
2010-02-20 23:22:30 補充：
更改:
故可設f(x)=(x-4)(3x-2)Q(x)+k(x-4)-5
由f(2/3)=15=-10k/3 -5得k=-6
所以,所求餘式為-6(x-4)-5即-6x+19。
2010-02-21 7:18 am
Let f(x)=(x-4)(3x-2)Q(x)+ax+b
sub x=4
4a+b=-5-----1
sub x=2/3
2/3+b=15-----2
2-1
-10/3a=20
a=-6
sub a=-6 into 1
b=19
so the remainder is -6x+19
sub x=4
4a+b=-5-----1
sub x=2/3
2/3+b=15-----2
2-1
-10/3a=20
a=-6
sub a=-6 into 1
b=19
so the remainder is -6x+19
收錄日期: 2021-04-23 20:41:14
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