Write a polynomial function in factored form with the given zeros at -10,-4,1

What you should see in this case is that you have a third degree polynomial because you have three different zeros.
 We have then that the generic form factorized for a polynomial of third degree is:
 (x-a) * (x-b) * (x-c)
 where,
 a, b, c: real numbers.
 For our case:
 (x + 10) * (x + 4) * (x-1)
 
 a polynomial function in factored form is
 (x + 10) * (x + 4) * (x-1)