Polynomial of Degree p:
- A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents.
- The degree of a polynomial is the highest power of the variable in the polynomial.
- A polynomial of degree p can be written as:
P(x) = a_px^p + a_{p-1}x^{p-1} + ... + a_1x + a_0

Number of Zeroes:
- Zeroes of a polynomial are the values of x for which the polynomial evaluates to zero.
- In other words, a value x is a zero of a polynomial if P(x) = 0.
- The number of zeroes of a polynomial can be equal to or less than the degree of the polynomial.

Option D - At most p zeroes:
- This option means that the polynomial can have a maximum of p zeroes.
- It indicates that the number of zeroes of the polynomial is not necessarily equal to the degree of the polynomial.
- Let's consider an example to understand this concept.

Example:
- Consider a polynomial of degree 3: P(x) = x^3 - 2x^2 + x - 1.
- We can find the zeroes of this polynomial by setting P(x) = 0 and solving for x.
- However, in this case, the polynomial may not have exactly 3 zeroes.
- It could have fewer zeroes depending on the nature of the polynomial.
- In this example, the polynomial has only 1 zero: x = 1.
- Therefore, this example illustrates that a polynomial of degree 3 can have at most 3 zeroes, but it may have fewer zeroes.

Conclusion:
- A polynomial of degree p can have at most p zeroes.
- The number of zeroes can be less than p, depending on the nature of the polynomial.
- Option D, "At most p zeroes," correctly describes the possible number of zeroes for a polynomial of degree p.