Answer
$f(x)=-\displaystyle \frac{1}{2}x^{3}-\frac{1}{2}x^{2}+x$
Work Step by Step
For any polynomial function $f(x),\ (x-k)$ is a factor of the polynomial if and only if $f(k)=0$.
So, we can write
$ f(x)=a(x+2)(x-1)(x-0)\quad$ for some number a.
To find $a,$ use the given information: $f(2)=-1$
$f(2)=a(-1+2)(-1-1)(-1-0)=-1$
$a(1)(-2)(-1)=-1$
$2a=-1$
$a=-1/2$
So,
$f(x)=-\displaystyle \frac{1}{2}(x+2)(x-1)(x-0)$
Rewrite in standard form
$f(x)=-\displaystyle \frac{1}{2}x(x^{2}+x-2)$
$f(x)=-\displaystyle \frac{1}{2}x^{3}-\frac{1}{2}x^{2}+x$