the common zero of the polynomial x3 +1 , x2-1 and x2+2x+1 is

x^3+1 = (x+1)(x^2-x+1) [ by using a^3+b^3 = (a+b)(a^2+b^2 - ab)]
x^2 - 1 = (x+1)(x-1)
And, x^2+2x+1 = x^2 +x+x+1 = (x+1)(x+1)
so, x^3+1 = (x+1)(x^2-x+1)
x^2 - 1 = (x+1)(x-1)
x^2+2x+1 = (x+1)(x+1)
so, here, (x+1) is a common factor of all these polynomial.
it means that -1 is a common zero of all these 3 polynomial.