Answer
$f(x)=\displaystyle \frac{1}{2}x^{3}-\frac{1}{2}x$
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-1)(x+1)(x-0)\quad$ for some number a.
To find $a,$ use the given information: $f(2)=3$
$f(2)=a(2-1)(2+1)(2-0)=3$
$a(1)(3)(2)=3$
$6a=3$
$a=1/2$
So,
$f(x)=\displaystyle \frac{1}{2}(x-1)(x+1)(x-0)$
Rewrite in standard form
$f(x)=\displaystyle \frac{1}{2}x(x^{2}-1)$
$f(x)=\displaystyle \frac{1}{2}x^{3}-\frac{1}{2}x$
