You can use synthetic division:
4 [ 8 7 5 -5 35 ]
32 156 644 2556
------------------------+
8 39 161 639 2591 <--- remainder
Explanation of synthetic division:
write out the coefficients of the powers of x, in the right order (8, 7, 5, -5 and 35)
Put 4 in front (the value of k)
the first coefficient, 8 goes straight down.
Multiply 4 with 8, put 32 in the next column. Add the numbers: 39
Multiply 4 with 39, put 156 in the next column. Adding gives 161.
Etc. the last number you get this way is the remainder!