Find the zeros of the polynomial

$f(x)=x^{2}-3 x-m(m+3)$

By adding and subtracting mx, we get

$f(x)=x^{2}-m x-3 x+m x-m(m+3)$

$=x[x-(m+3)]+m[x-(m+3)]$

$=[x-(m+3)](x+m)$

$f(x)=0 \Rightarrow[x-(m+3)](x+m)=0$

$\Rightarrow[x-(m+3)]=0$ or $(x+m)=0$

$\Rightarrow x=m+3$ or $x=-m$

So, the zeros of f(x) are −m and m + 3.