Use polynomial division or synthetic division to divide f(x) by (x+1).

Using synthetic division with root $-1$:

-1 | 1   6   11   6
   |    -1  -5  -6
   ----------------
     1   5    6   0

The quotient is $x^2 + 5x + 6$.

We need two numbers that multiply to 6 and add to 5. These are 2 and 3.

The final answer is $\boxed{(x+1)(x+2)(x+3)}$.

1. (ii) Let $\lambda$ be a real constant. Show that the roots of the quadratic equation $3x^2 + (-4-2\lambda)x = 0$ are always real.

For $3x^2 + (-4-2\lambda)x + 0 = 0$:
$a = 3$
$b = -4-2\lambda$
$c = 0$

For roots to be real, the discriminant must be greater than or equal to zero ($\Delta \ge 0$).
Since $(-4-2\lambda)^2$ is a square of a real number, it will always be greater than or equal to zero for any real value of $\lambda$.

Therefore, the roots of the quadratic equation are always real.