For n∈N,xn+1+(x+1)2n−1 is divisible by

For n=1, we have xn+1+(x+1)2n−1=x2+(x+1)=x2+x+1, which is divisible by  x2+x+1. For n = 2, we havexn+1+(x+1)2n−1=x3+(x+1)3=(2x+1)x2+x+1,which is divisible by x2+x+1. Hence, option (c) is true.