x^4 - 1 = x^4 + 0 x^3 + 0 x^2 + 0 x - 1
1 . | . 1 . 0 . 0 . 0 . -1
.... | ...... 1 . 1 . 1 .. 1
.... -----------------------
....... 1 . 1 . 1 . 1 .. 0
(x^4 - 1) / (x - 1) = (x^3 + x^2 + x + 1)
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NOTE: -1 is a zero of (x^3 + x^2 + x + 1), so you can use synthetic division again to find
(x^3 + x^2 + x + 1) / (x + 1)
-1 . | . 1 . 1 . 1 . 1
..... | ..... -1 . 0 . -1
..... ------------------
....... 1 .. 0 .. 1 .. 0
(x^3 + x^2 + x + 1) / (x + 1) = x^2 + 1