Division of polynomial - checking my answer.? [A level Mathematics]?

What is the quotient and remainder when x^4 +1 is divided by x^2 +1?

(If anyone isnt used to my terminoligy - ^ = to the power of)

Answers:
Provided my division is correct I got a quotient of x^2-1 and a remainder of 2.

Hope this helps. :)
........... 1x^2 + 0x - 1
.... ______________________
x^2 + 1 | x^4 + 0x^3 + 0x^2 + 0x + 1
.....x^4 + 0x^3 + 1x^2
........... 1x^2 + 0x + 1
........... 1x^2 + 0x - 1
........... 2

Therefore x^4 + 1 = (x^2 +1)(x^2 - 1) + 2
well i got x^2 remainder positive one. hopefully I'm right.
you're right smiley

x^2-1 with remainder 2
=(x+1)(x-1) with remainder 2
x^2-1
x^2+1\x^4+1
-x^4-x^2
-x^2
x^2+1
-1

so (x^4+1)/(x^2+1)=x^2-1 -1/(x^2+1)

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