Question 137471
division is:

...1...6....-2...-7
-1.....-1...-5...7
...1...5....-7...0
so the rest is 0
then yes x+1 is a factor of x^3+6x^2-2x-7

x^3+6x^2-2x-7=(x+1)(x^2+5x-7)