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 various linear expressions, we can use the Remainder Theorem. According to this theorem, the remainder of the division of a polynomial \( p(x) \) by \( g(x) = x - a \) is simply \( p(a) \).

Let's solve each part step by step:

### (i) Find the remainder when \( p(x) \) is divided by \( x + 1 \)

1. Set \( g(x) = x + 1 \).
2. Find \( a \) such that \( g(a) = 0 \):
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