Chapter 6 Polynomials

6.1 Adding Polynomials

6.1 Adding Polynomials Monomial – one term expression Binomial – two term expression…. Polynomial – “many terms” What is a Term? What does “like terms” mean?

The degree of a term is the power of the variable in that term… Determine the degree of the term: 3x 3x 3xy Determine the degree of the polynomial: 3x+5x+2 7x+2x+1

Rule for Adding Polynomials: Combine like terms! This means add or subtract the numbers (called coefficients) in front of the variables… Ex: 3x + 7x = 10x Ex: 5x + 6x² = 11x

Your Turn: (6x² + 5x -7) + (5x +2) (11xy-3y² - 4xy + 2) + (-6xy – 7xy + 4y² - 9) HW 6.1 #13-50 odd

6.2 Subtracting Polynomials

Agenda Warm-up 6.2 Subtracting Polynomials Practice subtracting 6.3 Multiplying Polynomials

Warm-up Simplify 3x² + 2x – 6 - 5x² - 7x -3

Subtracting polynomials: Distribute the negative sign.. Ex: (5x – 2) – (7x – 3) = 5x – 2 – 7x + 3 = -2x + 1

Your Turn: (12x + 5) – (9x – 11) (3x + 2x – 2) – (4x + 4x – 7) HW 6.2 #1-43 odd

6.3 Multiplying Monomials

Multiplying Monomials Remember, a monomial is a ONE term math expression Every monomial is the product of factors Ex: 6m²n = 2·3·m·m·n

Three Important Rules: Product of Powers: Power of a power: Power of a Product

Product of Powers: This is the idea that when multiplying polynomials, you add the exponents Ex: x·x = x Your turn: 3y·4y = ?

Power of a Power When raising a polynomial to a power, multiply Ex: (x)=x Your Turn: (m)=?

Power of a Product When raising a product to a power, distribute: Ex: (3a)² = 3²·a² = 9a² Your turn: (2pq)³ = ? HW: 6.3 #1 – 43 odd

6.4 Multiplying a Polynomial by a Monomial

Warm-Up (-x³y)² (-2ab²)³(5a²b³)² (3x)² - 7 + 2x² + 5

Multiplying a Polynomial by a Monomial: Use the distributive property… Ex. 1: 7x(5y + 7) = 7x·5y + 7x·7 = 35 xy + 49 x Ex. 2: 4x²(2yz + 5z) = 4x²·2yz + 4x²·5z = 8x²yz + 20x²z

Your Turn: 8m(9m² + 6m + 3) 2v³(12vp² - 7) -7x²y(-3x – 7y – 12) HW: 6.4 #1 – 31 odd

6.5 Multiplying Polynomials The FOIL Method

FOIL stands for: First – Outside – Inside – Last You should get four terms when multiplying two binomials. Your answer may only have three terms if you combine the two like terms.

FOIL: Ex.1: (x + 5)(x – 7) = x·x + x·7 + 5·x + 5·7 = x² +7x + 5x + 35

FOIL: Ex. 2: (2x – 1)(x + 8) = 2x·x + 2x·8 + (-1)·x + (-1)·8

Your Turn: (x + 3)(x + 2) (x + 2)(x – 2) (3x -5)² HW: 6.5 #1 – 43 odd

Agenda Warm-Up Homework Review 6.4 and 6.5 Practice Layers * Adding/Subtracting * Multiplying Monomials * FOILing

Warm-Up x³·x² (x + 3)(x – 4) (2x + 1)(x – 6)

6.6 Dividing Polynomials

Quotient Rules Think of a polynomial as the product of its factors…

Example: Simplifying Quotients

Example: Power of a Quotient

Divide a polynomial: Divide each term of the numerator by the denominator:

HW: 6.6 #1 – 29 odd