Find the remainder when `x^(3)+3x^(2)+3x+1` is divided by :
`(i) x+1 " " (ii) x-(1)/(2) " " (iii) x " " (iv) x+pi " " (v) 5+2x`

Explanation

To find the remainder when the polynomial \( P(x) = x^3 + 3x^2 + 3x + 1 \) is divided by different divisors, we will use the Remainder Theorem. According to this theorem, the remainder of the polynomial \( P(x) \) when divided by \( x - c \) is \( P(c) \).

Let's solve each part step by step:

### (i) When divided by \( x + 1 \)

1. **Set the divisor to zero**:
\[
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