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利用餘式定理,解4x^3 + 5x^2 - 3x + 3除以x^2 + 2x - 3的餘式
設f(x)=4x^3 + 5x^2 - 3x + 3
(4x^3 + 5x^2 - 3x + 3)除以x^2 + 2x - 3的餘式
2007-12-25 11:49 pm
回答 (3)
2007-12-25 11:56 pm
✔ 最佳答案
設f(x)=4x^3 + 5x^2 - 3x + 3 ,餘式為(ax+b) [低於除式一冪]f(x)=(x^2 + 2x - 3)Q(x)+(ax+b)
f(x)=(x+3)(x-1)Q(x)+(ax+b)---------1
把x=1代入1
f(1)=9=a+b---------2
把x=-3代入1
f(-3)=-51=-3a+b--------3
2-3:
4a=60
a=15,b=-6
所以餘式為(15x-6)
2007-12-26 12:11 am
(4x^3 + 5x^2 - 3x + 3) / (x^2 + 2x - 3)
Quotients : 4x - 3
Remainders : 15x - 6
I try to make u understand..
4x(x^2 + 2x - 3) - 3(x^2 + 2x - 3)
=4x^3 + 8x^2 - 12x - 3x^2 - 6x + 9
=4x^3 + 5x^2 - 18x + 9
R= (4x^3 + 5x^2 - 3x + 3) - (4x^3 + 5x^2 - 18x + 9)
= -3x + 18x + 3 - 9
= 15x - 6
Quotients : 4x - 3
Remainders : 15x - 6
I try to make u understand..
4x(x^2 + 2x - 3) - 3(x^2 + 2x - 3)
=4x^3 + 8x^2 - 12x - 3x^2 - 6x + 9
=4x^3 + 5x^2 - 18x + 9
R= (4x^3 + 5x^2 - 3x + 3) - (4x^3 + 5x^2 - 18x + 9)
= -3x + 18x + 3 - 9
= 15x - 6
參考: ME
2007-12-25 11:54 pm
....不明
收錄日期: 2021-04-25 17:17:50
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https://hk.answers.yahoo.com/question/index?qid=20071225000051KK01973