1. Chapter 6
Polynomials

3. 6.1 Adding Polynomials

4. 6.1 Adding Polynomials Monomial – one term expression
Binomial – two term expression….
Polynomial – “many terms”
What is a Term?
What does “like terms” mean?

5. 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

6. 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

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

8. 6.2 Subtracting Polynomials

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

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

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

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

13. 6.3 Multiplying Monomials

14. 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

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

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

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

18. 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

19. 6.4 Multiplying a Polynomial by a Monomial

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

21. 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

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

23. 6.5 Multiplying Polynomials
The FOIL Method

24. 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.

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

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

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

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

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

30. 6.6 Dividing Polynomials

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

32. Example: Simplifying Quotients

33. Example: Power of a Quotient

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

35. HW: 6.6 #1 – 29 odd