We can solve the problem by two methods: Synthetic division and long division.
Synthetic division:
-3 | 1 0 1 0 -2
-3 9 -30 90
---------------------------
1 -3 10 -30 88
The remainder is 88.
By long division:
h^3 -3h^2 + 10h -30
---------------------------------------
x + 3 | h^4 + 0h^3 + h^2 + 0h -2
h^4 + 3h^3
----------------
-3h^3 + h^2 + 0h -2
-3h^3 -9h^2
-------------------------------
10h^2 + 0h -2
10h^2 +30h
-----------------------
-30h - 2
-30h -90
--------------
88
The remainder is 88