how to divide x 4+1  by x2+1 ? and what will be the quotient & remainderx4 means x to the power 4 & x2 means x to the power 2

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We can find the quotient and remainder when x^4 + 1 is divided by x^2 + 1 using long division.

x^2 + 1 | x^4 + 1................| x^2 - 1

...............x^4 + x^2

-------------------------------------

.......................1 - x^2

......................-1 - x^2

------------------------------------

.......................2

 

The required quotient is x^2 - 1 and the remainder is 2.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

x^4+1 divided by x^2+1 = x^2 is quotient x^4+1- (x^2+1)x^2 = -x^2+1 is reminder.

-x^2+1 divided by x^2+1 = = -1 is quotient -x^2+1-(x^2+1)(-1) = 2 is reminder.

So x^4+1 divided by x^2+1 = x^2-1 quotient  and the remainder = 2.

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