It is given that -1 is one of the zeroes of the polynomial $x^3+2x^2-11x-12$ . find all the zeroes of the given polynomial.

Let $f(x)=x^3+2x^2-11x-12$

Given : $-1$ is a zero of the polynomial , which means $(x+1)$ is a factor of $f(x)$
 
Dividing $f(x)$ by $(x+1)$ we get

f(x) becomes:
$f(x)=(x+1)(x^2+x-12)$
$=(x+1)(x^2+4x-3x-12)$
$=(x+1)(x-3)(x-4)$

if $f(x)=0$
$\Rightarrow (x+1)(x-3)(x+4)=0$

either $(x+1)=0$ or $(x-3)=0$  or $(x+4)=0$

$x=-1$ or $x=3$ or $x=-4$

zeros of the polynomial are $-1,$ $3$ and $-4$