1. The problem: Understand what a polynomial means in mathematics. 2. A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents of variables. 3. For example, $$3x^2 + 2x - 5$$ is a polynomial where $3$, $2$, and $-5$ are coefficients and $x$ is the variable. 4. Polynomials can have one or more terms. Each term has a variable raised to a whole number exponent and a coefficient. 5. Polynomials are used to model many situations in algebra, calculus, and applied sciences. Final answer: A polynomial is a mathematical expression made up of variables and coefficients, using addition, subtraction, multiplication, and whole number exponents of the variables.