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 \( f(x) = x^3 + 3x^2 + 3x + 1 \) is divided by different linear factors, we can use the Remainder Theorem. According to this theorem, the remainder of the division of a polynomial \( f(x) \) by \( x - c \) is \( f(c) \).

Let's solve the problem step by step for each divisor:

### (i) Dividing by \( x + 1 \)

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