Chapter 6

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Chapter 6 - PowerPoint PPT Presentation

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….

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Chapter 6

Polynomials

• Monomial – one term expression
• Binomial – two term expression….
• Polynomial – “many terms”
• What is a Term?
• What does “like terms” mean?
• Determine the degree of the term:

3x

3x

3xy

• Determine the degree of the polynomial:

3x+5x+2

7x+2x+1

• 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
• (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

• (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
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

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

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

= x² + 12x + 35

FOIL:
• Ex. 2: (2x – 1)(x + 8)

= 2x·x + 2x·8 + (-1)·x

+ (-1)·8

= 2x² + 16x + (-1)x + (-8)

= 2x² + 15x - 8

• (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

* 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…
Divide a polynomial:
• Divide each term of the numerator by the denominator: