If p(x) is divisible by x-7, then there is no remainder. We could do this problem with relative ease by using synthetic division:
_____________
7 / 2 -11 c
14 21
-----------------------
2 3 0 c must = -21 for the remainder to be zero.
Now consider dividing the given poly by 2x+1. The corresponding root is -1/2
____________________
-1/2 / 2 3 -21
-1 -1
---------------------
2 2 -22 The remainder when p(x) is div. by 2x+1 is -22.
