Determine which of the following polynomials has \((x+1)\) a factor: (i) \( x^3 + x^2 + x + 1 \) (ii) \( x^4 + x^3 + x^2 + x + 1 \) (iii) \( x^4 + 3x^3 + 3x^2 + x + 1 \) (iv) \( x^3 - x^2 - \left(2 + \sqrt{2}\right)x + \sqrt{2} \)