Final answer:
The student seeks polynomials of degree n that only have x=0 as their zero. Any polynomial where x=0 makes it zero, like x^n, is a valid answer. The provided options are all correct examples of such polynomials.
Step-by-step explanation:
The student is asking to find a polynomial of degree n that has only the given zero(s). To find such a polynomial, we need to consider that if a polynomial has a zero at x, it means that x is a root of the polynomial. If we take the simplest case, a polynomial of degree n with a zero at x = 0, is x^n. Therefore, polynomials given in options A, B, C, and D all have a zero at x = 0 and are of different degrees (the highest power of x indicates the degree of the polynomial).
For example, consider option A x^5, which is a polynomial of degree 5 and has a zero at x = 0. Similarly, other options are also polynomials with various degrees having a zero at x = 0. However, without additional zeros provided or a specific degree n mentioned, any polynomial that can be constructed such that it equals zero when x = 0 would be an acceptable answer.