Question

What is the remainder when (x^4+36) is divided by (x^2-8)

Answer 1

100..........................

Answer 2

The remainder is 100.

Explanation:

The divisor is
`x^2-8`.

Dividend is
`x^4+36`.

We have to find the remainder of

`(x^4+36)/(x^2-8)`

It can be written as

`(x^4+36)/(x^2-8)=(x^4-64+64+36)/(x^2-8)`

`(x^4+36)/(x^2-8)=((x^4-64)+100)/(x^2-8)`

`(x^4+36)/(x^2-8)=((x^4-64))/(x^2-8)+(100)/(x^2-8)`

`(x^4+36)/(x^2-8)=((x^2-8)(x^2+8))/(x^2-8)+(100)/(x^2-8)`
`[\because a^2-b^2=(a-b)(a+b)]`

`(x^4+36)/(x^2-8)=x^2+8+(100)/(x^2-8)`

Therefore the remainder is 100.