1. Let's start by defining a polynomial. A **polynomial** is a mathematical expression consisting of variables (also called indeterminates) and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents of variables. 2. For example, a general polynomial in one variable $x$ can be written as: $$a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0$$ where $a_n, a_{n-1}, \ldots, a_0$ are coefficients, and $n$ is a non-negative integer (degree of the polynomial). 3. Polynomials can have one or more variables, such as $x$, $y$, $z$, and so on. For example: $$3x^2 + 2xy - 5y + 7$$ is a polynomial in variables $x$ and $y$. 4. Important characteristics of polynomials: - The exponents must be whole numbers (0, 1, 2, ...). - No division by variables is allowed (i.e., no negative or fractional exponents). - Operations involved are addition, subtraction, multiplication, and exponentiation to whole numbers. In summary, polynomials are expressions made from terms with variables raised to non-negative integers, multiplied by coefficients, and combined additively.