Maths Remainder Theorem
2010-06-26 9:42 pm
If the polynomial f(x) leaves a remainder of R when divided by (x+1), the polynomial f(x+1) leaves a remainder of R+1 when divided by (x+1).
Jusify the above statement.
回答 (3)
2010-06-26 10:34 pm
✔ 最佳答案
The statement is wrong.Let f(x) = x^2,
then
f(x) = x^2 = (x+1) * (x-1) + 1
here , R = 1 ;
But the polynomial
f(x+1) = (x+1)^2 = (x+1) * (x+1) + 0
here , the remainder = 0 not equal to R+1 = 1+1 .
2010-06-27 10:25 am
let the equation be f(x) = (x+1)
since it's divided by (x+1),
the factor will be -1 when the reminder is 0
R = -1+1 = 0
if the eqaution is f(x+1) = (x+2)
since it's divided by (x+1),
the factor will be -1 when the reminder is 0
R = -1+2 = 1
therefore, the statment is correct!
(my solution may wrong~)
since it's divided by (x+1),
the factor will be -1 when the reminder is 0
R = -1+1 = 0
if the eqaution is f(x+1) = (x+2)
since it's divided by (x+1),
the factor will be -1 when the reminder is 0
R = -1+2 = 1
therefore, the statment is correct!
(my solution may wrong~)
參考: N/A
2010-06-27 2:52 am
When f(x) is divided by (x+1) ,
f(x) = Q(x)(x+1)+R
When f(x+1) is divided by (x+1),
f(x+1) = Q(x+1)(x+1)+R
The statement is wrong
f(x) = Q(x)(x+1)+R
When f(x+1) is divided by (x+1),
f(x+1) = Q(x+1)(x+1)+R
The statement is wrong
收錄日期: 2021-04-21 22:20:34
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