Question 62976
Given that the polynomial has zeroes at 1, 2 and 4.

So the required polynomial will be :

a(x-1)(x-2)(x-4)

==> a(x-1)(x^2 - 2x - 4x + 8)

= a(x-1)(x^2 - 6x + 8)

= ax^3 - 6ax^2 + 8ax - ax^2 + 6ax - 8a

= ax^3 - 7ax^2 + 14ax - 8a

f(0) = - 8a

==> - 8a =  - 16
==> a = 2

Thus f(x) = 2x^3 - 14x^2 + 28x - 16
 is the required polynomial.

Good Luck!!!