x to the power of 2006, divided by x2-1 leaves the remainder????????? Pls explain!!!!!!

FIRST WRITE X TO POWER 2006 AS X-1+1 TO POWER 2006...DEN EXPAND IT USING BINOMIAL NEXPANSION...DEN  DIVIDE IT BY X2-1 ..U WL GET D ANS...

Dear student,

The remainder would be x raise to the power 2004

this is an example how to divide a polynomial function...

Example

Divide

        x⁴ + 3x² - 5
                               
            x² + 4x

Solution

We first write in long division form

Next decide what we need to multiply x² by to get x⁴.  Since 

        (x²)(x²)  =  x⁴ 

we can write

Next, we multiply x² + 7x and x².

Now subtract to get and bring down the 3x² to get

We repeat this process until the degree of the remainder is less than the degree of the denominator.

when x²⁰⁰⁶ is divided by x²-1 then remainder is x²⁰⁰⁴ by using this method ...

hi

i think the remainder is 1..............