On dividing x³ + 4x² + 5x + 6 by x, the remainder is :

1. 16

2. 6

3. -5

4. 5

On dividing x³ + 4x² + 5x + 6 by x, the remainder left is 6.

$\begin{array}{l} \phantom{xy}{x^2 + 4x + 5} \ x \overline{\smash{\big)}x^3 + 4x^2 + 5x + 6} \ \phantom{x}\underline{\underset{-}{}x^3} \ \phantom{{x}2x^3+}4x^2 \ \phantom{{x}x^3+}\underline{\underset{-}{}4x^2} \ \phantom{{x}x^3+2-5x^2}5x \ \phantom{{x}x^3+2-x1}\underline{\underset{-}{}5x} \ \phantom{{x}x^3+2-5x^23-3}6 \ \phantom{{x}x^3+2-5x^23-3}\underline{0} \ \phantom{{x}x^3+2-5x^23-3}6 \end{array}$

Hence, Option 2 is the correct option.