Preliminary Explanation:
A polynomial of degree one is a linear polynomial, which means it can be written in the form p(x) = mx + b, where m and b are constants. The term "zero" of a polynomial refers to the value of x that makes the polynomial equal to zero. In this case, if p(a) = 0, it means that when the value of x is a, the polynomial evaluates to zero. Therefore, a is called the "zero" of p(x).

Detailed Explanation:
To understand why the correct answer is option A, we can break down the given information and the definitions of the terms involved:

1. Polynomial of Degree One:
- A polynomial is an algebraic expression consisting of variables and coefficients combined using addition, subtraction, and multiplication.
- The degree of a polynomial is the highest power of the variable in the expression.
- A polynomial of degree one is called a linear polynomial, represented by p(x) = mx + b, where m and b are constants.

2. Zero of a Polynomial:
- The zero of a polynomial is the value of x that makes the polynomial equal to zero.
- In other words, if p(a) = 0, it means that when the value of x is a, the polynomial evaluates to zero.

Given that p(x) is a polynomial of degree one and p(a) = 0, we can conclude the following:

- Since p(x) is a linear polynomial, it can be written as p(x) = mx + b.
- Substituting x = a into the polynomial, we have p(a) = ma + b.
- The given condition p(a) = 0 implies that ma + b = 0.
- Solving this equation for a, we get a = -b/m.

Therefore, the value of x, which is a, that makes the polynomial p(x) equal to zero is called the "zero" of p(x). Hence, the correct answer is option A: Zero of p(x).

Summary:
In summary, when a polynomial of degree one (linear polynomial) is given and it is stated that p(a) = 0, the value of x, denoted as a, is called the "zero" of p(x). This means that when x is equal to a, the polynomial evaluates to zero.