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-(2+sqrt(2))x+sqrt(2)`

Explanation

To determine which of the given polynomials has \( (x + 1) \) as a factor, we will use the Factor Theorem. According to the Factor Theorem, \( (x + 1) \) is a factor of a polynomial \( p(x) \) if and only if \( p(-1) = 0 \).

We will evaluate each polynomial at \( x = -1 \).

### Step-by-Step Solution:

1. **Evaluate the first polynomial:**
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