Simple polynomial division question

Hello

I hope someone can help me with this.

Let's say I want to divide x^2 + x + 1 into x^2 + 1

Am I right in thinking the answer is 1 remainder x?

This is how I am getting my answer...

I convert my polynomials into binary -

x^2 + x + 1 = 111

x^2 + 1 = 101

Then I do long division -

Code:

` 1`

111 / 101

111

----

010

Which translates as 1 remainder x.

Am I correct?

If so, how would I handle x^4 + 1 into x^2 + 1?

Convert to binary -

10001 / 101

Am I right in thinking the answer is -

Code:

` 0`

10001 / 101

000

----

101

So the answer is 0 remainder x^2 + 1?

Thank you.