divide x^4 - x^3 + x^2 -1 by x - 1 and check.?

Answer 1

x^3 + 1 remainder x+1
====================
Ooops, did it wrong,
The guy above is correct.
x^3 + x + 1

Answer 2

1 -1 1 0 -1 /1
1 0 1 1
______________________
1 0 1 1 0

answer is x^3 + x + 1

Answer 3

Using synthetic division:-

1|1___-1___1___0___-1
_|____1____0___1___1
_|1___0____1___1___0

x^4 - x³ + x² - 1
-------------------- = x³ + x + 1
(x - 1)