Question

multiplying polynomials notes n12
polynomial - an expression with one or more _______ that are joined by addition,
subtraction, and multiplication
example: $12y^2 + 5y - 3$
monomial - a polynomial with ______ term
example: $6x^3$
binomial - a polynomial with ______ terms
example: $x^2 + 7$
distributive property - multiplying a term by _______ terms
example: $3x^2(2x^4 - 5)$

multiplying monomials by polynomials

Explanation:

1. For "polynomial", a polynomial is an expression with one or more terms (since terms are the parts joined by +, -, ×; e.g., \(12y^2\), \(5y\), \(-3\) in \(12y^2 + 5y - 3\)).
2. "monomial" is a polynomial with one term (e.g., \(6x^3\) has only one term).
3. "binomial" is a polynomial with two terms (e.g., \(x^2 + 7\) has two terms: \(x^2\) and \(7\)).
4. "distributive property" involves multiplying a term by each term inside a polynomial (e.g., \(3x^2(2x^4 - 5) = 3x^2 \cdot 2x^4 - 3x^2 \cdot 5\), so multiplying by each term in \(2x^4 - 5\)).

Answer:

• polynomial: terms
• monomial: one
• binomial: two
• distributive property: each