Which one of the following is a factor of $$x^3 + 6x^2 + 11x + 6?$$

As per the given equation,

$$x^3 + 6x^2 + 11x + 6=0$$
If the given options are satisfying the equation then it will give zero.
x-1=0, so x =1 putting in the equation,

$$\Rightarrow x^3 + 6x^2 + 11x + 6=0$$

$$\Rightarrow 1+6+11+6 \neq 0$$

Now, trying option b, x-2=0 , so x=2

$$\Rightarrow x^3 + 6x^2 + 11x + 6=0$$

$$\Rightarrow 8+24+22+6 \neq0$$

Now, putting option c, x+3=0, x=-3

$$\Rightarrow (-3)^3+6\times (-3)^2+11\times (-3)+6=0$$

$$\Rightarrow -27+54-33+6=0$$

Hence it is satisfying the condition.

Now, putting option D, x-3=0, x=3

$$\Rightarrow x^3 + 6x^2 + 11x + 6=0$$

$$\Rightarrow 27+54+33+6\neq 0$$

Hence, option C is the correct answer.