1 / 35

Chapter 6

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….

abeni
Download Presentation

Chapter 6

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 6 Polynomials

  2. 6.1 Adding Polynomials

  3. 6.1 Adding Polynomials • Monomial – one term expression • Binomial – two term expression…. • Polynomial – “many terms” • What is a Term? • What does “like terms” mean?

  4. 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

  5. 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

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

  7. 6.2 Subtracting Polynomials

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

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

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

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

  12. 6.3 Multiplying Monomials

  13. 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

  14. Three Important Rules: • Product of Powers: • Power of a power: • Power of a Product

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

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

  17. 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

  18. 6.4 Multiplying a Polynomial by a Monomial

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

  20. 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

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

  22. 6.5 Multiplying Polynomials The FOIL Method

  23. 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.

  24. FOIL: • Ex.1: (x + 5)(x – 7) = x·x + x·7 + 5·x + 5·7 = x² +7x + 5x + 35 = x² + 12x + 35

  25. FOIL: • Ex. 2: (2x – 1)(x + 8) = 2x·x + 2x·8 + (-1)·x + (-1)·8 = 2x² + 16x + (-1)x + (-8) = 2x² + 15x - 8

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

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

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

  29. 6.6 Dividing Polynomials

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

  31. Example: Simplifying Quotients

  32. Example: Power of a Quotient

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

  34. HW: 6.6 #1 – 29 odd

More Related