Final answer:
One zero of the cubic function f(x)=x³-14x+8 is given as -4. To find the remaining zeros, the synthetic division should be used to simplify the cubic to a quadratic, and then the quadratic formula or factoring can be utilized to find the rest of the zeros.
Step-by-step explanation:
The student is asked to list all zeros of the function f(x)=x³-14x+8, given that f(-4)=0. One zero of the function is already given: -4. To find the rest of the zeros, we would typically factor the cubic function or use synthetic division. Since we only have one zero, we cannot directly apply the quadratic formula here because the function is cubic, not quadratic.
We'll proceed by performing synthetic division with the known zero -4 to simplify the cubic to a quadratic. Then, we use the resultant quadratic to find the remaining zeros. If this was a homework or exam question, the student should complete these steps to find the other zeros.