Answer
$f(x)=-3x^{3}+6x^{2}+33x-36$
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+3)(x-1)(x-4)\quad$ for some number a.
To find $a,$ use the given information: $f(2)=30$
$f(2)=a(2+3)(2-1)(2-4)=30$
$a(5)(1)(-2)=30$
$-10a=30$
$a=-3$
So,
$f(x)=-3(x+3)(x-1)(x-4)$
Rewrite in standard form
$f(x)=-3(x+3)(x^{2}-5x+4)$
$=-3[x(x^{2}-5x+4)+3(x^{2}-5x+4)]$
$=-3(x^{3}-5x^{2}+4x+3x^{2}-15x+12)$
$=-3(x^{3}-2x^{2}-11x+12)$
$f(x)=-3x^{3}+6x^{2}+33x-36$
