Answer:
To divide (-5k² + k³ + 8k + 4) by (-1 + k), we can use long division.
lua
k^2 - 7k + 1
---------------------
-1 + k | k^3 - 5k^2 + 8k + 4
-k^3 + k^2
-------------
-4k^2 + 8k
+4k^2 - 4k
------------
4k + 4
Therefore, (-5k² + k³ + 8k + 4) ÷ (-1 + k) = k^2 - 7k + 1 with a remainder of 4k + 4.