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)

answer:

a polynomial function in factored form is

(x + 10) * (x + 4) * (x-1)