Answer
$f(x)=-3x(x+1)(x-2)$
Work Step by Step
It is given that $f(-1)=f(0)=f(2)=0$. Therefore, there must be a zero at x = -1, 0 and 2.
Now, we know that the equation is a $cubic function$. We already have 3 roots, and hence we can write the equation as $f(x)=ax(x+1)(x-2)$.
The last step is to find $a$ in order to find the final expression. This is done through using $f(1)=6$.
Like so:
$f(1) = a(1)(1+1)(1-2)$
$f(1)=-2a$
But$f(1)=6$ so,
$-2a=6$ which leads to $a=-3$
Which then leads to our final answer: $f(x)=-3x(x+1)(x-2)$
