In Exercises 9–22, multiply the monomial and the polynomial.5x³ (2x⁵−4x²+9)

A monomial is a single term algebraic expression that consists of a coefficient and one or more variables raised to non-negative integer powers. For example, in the expression 5x³, 5 is the coefficient and x is the variable raised to the power of 3. Understanding monomials is essential for performing operations like multiplication with polynomials.

A polynomial is an algebraic expression that consists of multiple terms, each of which is a monomial. Polynomials can be classified by their degree, which is the highest power of the variable in the expression. In the given example, 2x⁵ - 4x² + 9 is a polynomial with three terms, and recognizing its structure is crucial for correctly applying multiplication with a monomial.

The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term in a polynomial. This property is fundamental when multiplying a monomial by a polynomial, as it ensures that each term in the polynomial is multiplied by the monomial separately, leading to the correct expansion of the expression.