Overview
This lecture covers how to multiply and divide binomials and multinomials using distributive, FOIL, and vertical methods, including worked examples and practice activities.
Multiplying Monomials by Polynomials
- A monomial has one term; a binomial has two; a trinomial has three; a multinomial has more than three.
- To multiply a monomial by a polynomial, distribute the monomial to each term of the polynomial.
- For variables with the same base, add their exponents when multiplying.
- Combine like terms only if variables and exponents match.
Dividing Polynomials by a Monomial
- Divide each term of the polynomial (dividend) by the monomial (divisor) separately.
- For coefficients, divide the numbers; for variables with the same base, subtract the exponents.
- Keep the operation signs as in the original polynomial.
- Combine like terms only if variables and exponents match.
Multiplying Binomials (Distributive, FOIL, Vertical Methods)
- Distributive Property: Multiply each term in the first binomial by each term in the second, then combine like terms.
- FOIL Method: Multiply terms in this order: First, Outer, Inner, Last.
- Example: (x + 8)(x + 3) → x² + 11x + 24.
- Vertical Method: Align the binomials vertically and perform multiplication similar to long multiplication; add like terms to get the result.
Practice and Activities
- Practice multiplying and dividing polynomials using the provided examples.
- Try each method for multiplying binomials and check answers against the solutions shown.
Key Terms & Definitions
- Monomial — a polynomial with one term (e.g., 3x).
- Binomial — a polynomial with two terms (e.g., x + 4).
- Trinomial — a polynomial with three terms.
- Multinomial — a polynomial with more than three terms.
- Distributive Property — multiplying one term by each term inside a parenthesis.
- FOIL Method — a technique for multiplying two binomials: First, Outer, Inner, Last.
- Vertical Method — a way of multiplying polynomials arranged vertically, similar to long multiplication.
Action Items / Next Steps
- Complete the practice activity for multiplying and dividing polynomials by monomials.
- Practice binomial multiplication using distributive, FOIL, or vertical methods and check your work with provided answers.
- Review key terms and definitions before the next lesson.