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

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

Grade:9

4 Answers

T.MANI TEJA
34 Points
11 years ago

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...

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

Dear student,

The remainder would be x raise to the power 2004

vikas askiitian expert
509 Points
11 years ago

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.

        Poly Division

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


iit jee
44 Points
11 years ago

hi

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

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