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 can use the Factor Theorem. According to the Factor Theorem, \( (x + 1) \) is a factor of a polynomial \( P(x) \) if \( P(-1) = 0 \).

Let's evaluate each polynomial at \( x = -1 \).

### Step 1: Evaluate the first polynomial \( P_1(x) = x^3 + x^2 + x + 1 \)

1. Substitute \( x = -1 \):
\[
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