Question 44650
We know that: 
{{{f(1)=0}}},
{{{f(2)=0}}},
{{{f(4)=0}}}.
And the Highest power of x is cubed {{{x^3}}}
This step is pretty simple just put in brackets (x-a) where a is the value of x where f(x)=0 (i.e. f(a)=0):
{{{f(x)=b(x-1)(x-2)(x-4)}}} (Don't worry, the value of "b" is about to become clearer).
We also know that when x=0, f(x)=-16. Try to find the value of f(0) with our previous equation:
{{{f(0)=b(-1)(-2)(-4)=16}}}
{{{-8b=-16}}}
so b=2.
Now we can write the function:
{{{f(x)=2(x-1)(x-2)(x-4)}}}
here's the graph of y=f(x):
{{{ graph( 300, 200, -6, 5, -20, 10, 2(x-1)(x-2)(x-4)) }}} 
I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam