1) 若多項式 Q(x) 能被 x+1 整除, 問下列哪個數式必為 Q(x-1) 的因式?
A) x-1
B) x (答案)
C) x+1
D) x+2
2)當多項式 p(x) 除以 x-1 和 x+1 時,所得的餘數分別是 1 和 3 .求當 p(x) 除以 x的二次方-1 時所得的餘數(式)
A) 4
B) -x+2 (答案)
C) x+3
D) 3x+1
我需要列式!!
各位,求救(2題)
2006-11-23 5:41 am
回答 (2)
2006-11-25 2:44 am
✔ 最佳答案
1) Q(X) 能被 X+1 整除
Q(X) =(X+1)*P(X)
X=x-1
Q(x-1) =((x-1)+1)*P(x-1) = x * P(x-1)
(答案(B) x)
2)
p(x) = (x-1)(x+1)Q(x) + ax + b......(餘數(式) = ax+b, 求a,b)
p(1) = ((1)-1)((1)+1)Q(-1) + a(1) + b = 1 和
p(-1)= ((-1)-1)((-1)+1)Q(-1) + a(-1) + b=3
p(1) = a+b = 1 和
p(-1) = -a+b = 3
a=(1-3)/2=-1
b=(1+3)/2=2
答案: ax+b = -1 * x + 2 = -x + 2
2006-11-23 7:37 am
(a) Let y=x-1, the x = (x-1)+1 = y+1 is a factor of Q(y) = Q(x-1)
(b) For this is a MC question, I will just put x=1 and x= -1 into the choices listed to order to obtain the value 1 and 3 respectively.
Otherwise, we should have 1=p(1)=A(1)+B and 3=p(-1)=A(-1)+B . Solving for A and B, we have A= -1 and B = 2.
(b) For this is a MC question, I will just put x=1 and x= -1 into the choices listed to order to obtain the value 1 and 3 respectively.
Otherwise, we should have 1=p(1)=A(1)+B and 3=p(-1)=A(-1)+B . Solving for A and B, we have A= -1 and B = 2.
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