Day 1 – Polynomials Multiplying Mrs. Parziale

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Presentation transcript:

Day 1 – Polynomials Multiplying Mrs. Parziale Factoring Unit Day 1 – Polynomials Multiplying Mrs. Parziale

Introducing Polynomials Term Definition Monomial Is a number, a variable, or a product of a number and one or more variables with whole number exponents. 8 -2x 3x2y Polynomial Is a monomial or a sum of monomials 4x2 3x2 + 4x + 5 Binomial A polynomial with 2 terms x – 4 4y2 + 8 Trinomial A polynomial with 3 terms x2 – 3x + 10

Definitions Degree of a polynomial – the highest sum of exponents for any one monomial of the polynomial. Find the degree of the given polynomial.

More Definitions The leading coefficient of a polynomial is the coefficient of the variable with the ____________ exponent. The constant term of a polynomial is the term __________________. largest without a variable

Yet Another Definition Standard form of a polynomial is when the terms are written so that the exponents on the variables decrease from left to right.

Try These Write the polynomial in standard form. Identify the leading coefficient and constant terms of each.

Multiplication of Polynomials Part 1: Monomial x Monomial

Part 2: Monomial x Polynomial

Part 3: Binomial x Binomial Distribute, then combine like terms (FOIL)

Part 4: Polynomial x Polynomial Use the distributive property.

Multiplying Special Polynomials Special Product #1: Sum and Difference of 2 Terms What is the pattern? (a + b)(a – b) = ___________

Multiplying Special Polynomials 4. Special Product #2: The Square of a Binomial What is the pattern? (a + b)2 = _______________ What is the pattern? (a - b)2 = _______________

Closure What is the degree of a polynomial? What is a monomial, binomial, trinomial, polynomial? How do you multiply polynomials? How do you multiply special polynomials, such as: