The given expression has no rational zeroes, which would be required for synthetic division.
I suggest that the expression should have been x4-8x3+7x2+2x-14. When x=-1 this evaluates to:
1+8+7-2-14=0 so x=-1 is a zero. Now we can use synthetic division to reduce to a cubic:
-1 | 1 -8 7 2 -14
1 -1 9 -16 | 14
1 -9 16 -14 | 0 = x3-9x2+16x-14.
14=1×14=2×7, so ±7 or ±2 may be zeroes. So try ±2:
±8-36±32-14 which gives us either -10 or -90. So this is not a zero.
Now try ±7: ±343-441±112-14 which gives us either 0 or -910, therefore 7 is a zero.
Use synthetic division again:
7 | 1 -9 16 -14
1 7 -14 | 14
1 -2 2 | 0 = x2-2x+2 and we can find the complex zeroes:
x2-2x=-2, x2-2x+1=-1, (x-1)2=-1, x=1±i where i=√-1.
So the zeroes are -1, 7, 1+i, 1-i.