The remainder after dividing by x-1 is k+12, so k+12=-6 and k=-18.
The remainder after dividing by x+1 is k-12=-30.
The Remainder Theorem tells us that the remainder after dividing by x-1 is p(1)=1-2+13+k=k+12.
Similarly, for x+1 it's p(-1)=-1+2-13+k=k-12.