Final answer:
The polynomial 3 - (1/2)x has a degree of 1, its leading coefficient is -(1/2), and the constant term is 3. These terms help describe the polynomial's graph and are important in various algebraic methods.
Step-by-step explanation:
Finding Degree, Leading Coefficient, and Constant Term
To solve the mathematical problem of finding the degree, leading coefficient, and constant term of a polynomial like 3 - (1/2)x, we must first understand the structure of a polynomial. A polynomial is made up of terms, each with a coefficient (number in front) and a variable (like x) raised to an exponent (the degree). The degree of the polynomial is the highest exponent of the variable, the leading coefficient is the coefficient of the term with the highest exponent, and the constant term is the term without a variable.
In the given polynomial 3 - (1/2)x, the term -(1/2)x has an exponent of 1 on the x (implied as x^1), and the term 3 is a constant with no variable attached. Therefore, the degree of the polynomial is 1, because that is the highest exponent. The leading coefficient here is -(1/2), because it is the coefficient associated with the highest degree. The constant term is 3, as it is the term without a variable.
It's important to understand these components to give a 500 word answer or solve any polynomial-related problems fully. They help to describe the shape and characteristics of the graph of the polynomial, and are pivotal when applying various algebraic methods such as factoring or solving polynomial equations.