Question

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Answer 1

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.