Factoring Unit

Day 1 – PolynomialsMultiplying

Mrs. Parziale

Introducing PolynomialsTerm 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 monomials4x2 3x2 + 4x + 5

Binomial A polynomial with 2 terms x – 4 4y2 + 8

Trinomial A polynomial with 3 termsx2 – 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.

1. 3 2x 32. 4 17 5x x

3 23. 7 10 15x y xy

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.

2 34. 3 3 12x x x 3 25. 4 3x x

2 36. 7 6 3x x x

Multiplication of Polynomials

• Part 1: Monomial x Monomial

3 47. ( )( )x x

3 2 5 28. ( )( )a b ab

Part 2: Monomial x Polynomial

29. 5 ( 2 3)x x x

3 210. 4 (2 5 9)x x x

Part 3: Binomial x Binomial

• Distribute, then combine like terms (FOIL)

11. (6 5)(3 4)x x 212. ( 4 )( 1)x x x

Part 4: Polynomial x Polynomial

• Use the distributive property.

313. (3 2)(2 2 1)x x x

314. ( 5)(4 3 7)a a a

Multiplying Special Polynomials

Special Product #1: Sum and Difference of 2 Terms

1. ( 4)( 4)x x 2 22. ( 3)( 3)x x

What is the pattern? (a + b)(a – b) = ___________

Special Product #2: The Square of a Binomial

Multiplying Special Polynomials

23. (5 3)x 24. (3 7)x

4.

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:

( 6)( 6)x x 2( 7)x 2( 7)x