math problem help needed!

[darkforce]

let f(x) be a polynomial such that the remainder when f(x) is divided by x+1 is 1 and the remainder when f(x) is divided by x-1 is 3. Find the remainder when f(x) is divided by (x+1)(x-1).

 

[任天翔]

好像不难, 不过我有事,帮你顶一下贴好了

 

[darkforce]

thx~

we know that f(-1) = 1
and f(1) = 3

 

[难波万]

x+2 ?

 

[猫罐头]

根号3

 

[darkforce]

well...why??
how did you do it.

 

[寂寞很吵]

f(x)=x+2

 

[darkforce]

but we are trying to Find the remainder when f(x) is divided by (x+1)(x-1).

 

[难波万]

that's right~when f(x)=x+2, the remainder will also be x+2....
or im wrong?

 

[darkforce]

well, it's suppose to be a number...

 

[darkforce]

we are trying to find f[(x+1)(x-1)]

 

[难波万]

don't get the question~~

i thought it's f(x)/(x+1) = y + 1/(x+1) and f(x)/(x-1) = z + 3/(x-1)
y and z can be any whole number solved by f(-1) = 1 and f(1) = 3, y = z = 1~

then....f(x)=x+2...



what is f[(x+1)(x-1)]...

 

[猫罐头]

错了得+_根号3
f(x)=(x-1)(?)(x+1)

f(x)/(x-1)=3 f(x)/(x+1)=1

f(x)=3(x-1)=(?)(x+1) f(x)=(x+1)=(?)(x-1)

两式相乘3(x-1)(x+1)=(?)^2(x-1)(x+1); (?)^2=3;(?)=+ - 根号3

 

[darkforce]

sorry, we are trying to find f(x)/[(x+1)(x-1)]

 

[darkforce]

or in other words

f(x)/(x^2-1) find the remainder