If the polynomial x³³ - x²² + 3 is divided by x + 1 = 0, the remainder is :

1. -1

2. 1

3. 3

4. 2

By remainder theorem,

If f(x), a polynomial in x, is divided by (x - a), the remainder = f(a).

Given,

⇒ x + 1 = 0

⇒ x = -1.

Substituting value in x³³ - x²² + 3, we get :

⇒ (-1)³³ - (-1)²² + 3

⇒ -1 - 1 + 3

⇒ 1.

Hence, Option 2 is the correct option.