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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

Chapter 6

Polynomials

6 1 adding polynomials4
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
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
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
Your Turn:
  • (6x² + 5x -7) + (5x +2)
  • (11xy-3y² - 4xy + 2)

+ (-6xy – 7xy + 4y² - 9)

  • HW 6.1 #13-50 odd
agenda
Agenda
  • Warm-up
  • 6.2 Subtracting Polynomials
  • Practice subtracting
  • 6.3 Multiplying Polynomials
warm up
Warm-up
  • Simplify 3x² + 2x – 6 - 5x² - 7x -3
subtracting polynomials
Subtracting polynomials:
  • Distribute the negative sign..
  • Ex: (5x – 2) – (7x – 3)

= 5x – 2 – 7x + 3

= -2x + 1

your turn12
Your Turn:
  • (12x + 5) – (9x – 11)
  • (3x + 2x – 2) – (4x + 4x – 7)
  • HW 6.2 #1-43 odd
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
Three Important Rules:
  • Product of Powers:
  • Power of a power:
  • Power of a Product
product of powers
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
Power of a Power
  • When raising a polynomial to a power, multiply
  • Ex: (x)=x
  • Your Turn: (m)=?
power of a product
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
warm up20
Warm-Up
  • (-x³y)²
  • (-2ab²)³(5a²b³)²
  • (3x)² - 7 + 2x² + 5
multiplying a polynomial by a monomial
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 turn22
Your Turn:
  • 8m(9m² + 6m + 3)
  • 2v³(12vp² - 7)
  • -7x²y(-3x – 7y – 12)
  • HW: 6.4 #1 – 31 odd
foil stands for

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.

slide25
FOIL:
  • Ex.1: (x + 5)(x – 7)

= x·x + x·7 + 5·x + 5·7

= x² +7x + 5x + 35

= x² + 12x + 35

slide26
FOIL:
  • Ex. 2: (2x – 1)(x + 8)

= 2x·x + 2x·8 + (-1)·x

+ (-1)·8

= 2x² + 16x + (-1)x + (-8)

= 2x² + 15x - 8

your turn27
Your Turn:
  • (x + 3)(x + 2)
  • (x + 2)(x – 2)
  • (3x -5)²
  • HW: 6.5 #1 – 43 odd
agenda28
Agenda
  • Warm-Up
  • Homework Review 6.4 and 6.5
  • Practice Layers

* Adding/Subtracting

* Multiplying Monomials

* FOILing

warm up29
Warm-Up
  • x³·x²
  • (x + 3)(x – 4)
  • (2x + 1)(x – 6)
quotient rules
Quotient Rules
  • Think of a polynomial as the product of its factors…
divide a polynomial
Divide a polynomial:
  • Divide each term of the numerator by the denominator: