check whether (x+1) is a factor of x3+x2+x+1
Let f(x) = x3+x2+x+1
According to remainder theorem, if f(x) divided by x+1, then f(-1) is remainder. (-1 is the 0 of the polynomial x+1)
So replace x everywhere with -1
F(-1) = -1+1-1+1 = 0
Since remainder is 0, x+1 is factor of x3+x2+x+1