Question 467453
-1 a root means x + 1 is a factor of the polynomial
2 a root means x - 2 is a factor of the polynomial
3 a root means x - 3 is a factor of the polynomial

==> The polynomial is of the form f(x) = a(x+1)(x-2)(x-3), where a is an undetermined coefficient.  To find the value of c, use the boundary condition f(0) = 18.

==> f(0) = c(0+1)(0-2)(0-3) = c*1*-2*-3 = 6c = 18 ==> c = 3.

Hence the polynomial is f(x) = 3(x+1)(x-2)(x-3).  I leave it up to you to multiply out the linear factors.