中四數學-商式,餘式,被除式

2008-12-26 9:50 pm

1.求下列各題的商式和餘式
(a)(x^3-x^2+x-1)/(x-1)
(b)(3x^3-x^2+5x-2)/(x+3)

2.求下列各題的被除式
(a)除式=(x-2) 商式=(3x-1) 餘式=1
(b)除式=(x^2-1) 商式=(x+2) 餘式=0

3.已知多項式f(x)=x^3-2x^2+1。利用餘式定理求f(x)被下列各除式相除時所得的餘式
(a)(x-1)

4.利用因式定理判斷下列各式是否多項式f(x)=3x^3+11x^2+5x-3
(a) (x+1)
(b) (x+3)

5. 求下列各題的商式和餘式
(a) (3-x+2x^2-x^3)/(x^2-2x+2)
(b) (1-x+3x^3)/(x^2-3x)

回答 (1)

alicia

2008-12-27 5:03 am

✔ 最佳答案

1.(a)
商式 = x^2 + 1
餘式 = 0
(b)
商式 = 3x^2 - 10x + 35
餘式 = 107
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2.(a)
(x - 2)(3x - 1) + 1
= 3x^2 - x - 6x + 2 + 1
= 3x ^2 - 7 x + 3
(b)
(x^2 - 1)(x + 2)
= x^3 + 2x^2 - x - 2
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3.
f(x)=x^3 - 2x^2 + 1
(a)
(x - 1)
f(1)=(1)^3 - 2(1)^2 + 1
= 1 - 2 + 1
= 0
i.e. 餘式 = 0
_____________________________________
4.
f(x)=3x^3 + 11x^2 + 5x - 3
(a)
(x+1)
f(-1)=3(-1)^3 + 11(-1)^2 + 5(-1)-3
= -3 + 11 + 5 - 3
= 0
i.e.(x+1)是多項式f(x)=3x^3 + 11x^2 + 5x - 3的商式
(b)
(x+3)
f(-3)=3(-3)^3 + 11(-3)^2 + 5(-3)-3
=-81 + 99 - 15 - 3
= 0
_____________________________________
5.
(a)
(3 - x + 2x^2 - x^3) / (x^2 - 2x + 2)
商式 = -x
餘式 = x + 1
(b)
(1 - x + 3x^3) / (x^2 - 3x)
商式 = 3x
餘式 = 9x^2 - x + 1

參考: me.

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