Question

find a third degree polynomial function such asf(0)=-12 and whose zeroes are 1,2,3

Answer 1

start with
\[f(x)=a(x-1)(x-2)(x-3)\] and solve for \(a\) by noting that
\[f(0)=a(0-1)(0-2)(0-3)=-6a=-12\]

Answer 2

2(x-1)(x-2)(x-3)

Answer 3

this gives you \(a=2\) so it is going to be
\[f(x)=2(x-1)(x-2)(x-3)\] multiply out if you like