1 / 127

Understanding Polynomials: Multiplying and Dividing Monomials

Learn to identify and simplify monomials, multiply and divide powers, deal with negative exponents, and master polynomials in descending order. Practice exercises included.

williamnelson
Download Presentation

Understanding Polynomials: Multiplying and Dividing Monomials

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. Chapter5A:Polynomials Algebra 2A -2012

  2. Lesson 5.1A • I can identify the base and the exponent. • I can simplify product of monomials.

  3. What is it? Examples: bn Power Nonexamples: Important characteristic: Base: ____ Exponent: ____ Shortcut for repeated multiplications

  4. Example 1: Simplify the following (6x2)(x4) (45)(42) (3x4y)(-4x2) a. b. c.

  5. Your Turn 1: Simplify the following (23)(24) (5v4)(3v) (-4ab6)(7a2b3) 1. 2. 3.

  6. What is it? Examples: x3• x4 bn• bm = bn + m same bases (2x3y)(5x) Product of Powers Nonexamples: Important characteristic: Add the exponents x3 • x4≠ x12

  7. I can simplify product of Powers. Example 2: Simplify the following a. b. c. (3xy)2 (x5)2 (y7)3

  8. Your Turn 2: Simplify the following (m 6)2 (2b2)4 (4abc)2 1. 2. 3.

  9. Example 3: Simplify the following (10ab4)3 (3b2)2 d.

  10. Your Turn 3: Simplify the following (2xy2)3 (-4x5)2 4.

  11. I can simplify quotient of monomials. Example 4 a.16x3y4 4 x5y b.

  12. Your Turn! (3xy5)2 (2x3y7)3

  13. Homework: Lesson 5.1 A Check your answers !

  14. Lesson 5.1B • I can simplify quotient of monomials. • I can simplify monomials with negative exponents. • I can simplify monomials with a zero exponent.

  15. (5xy)0 = 1 (b)0 = 1 Zero Exponents 8-2 Anything to the power of zero is one! (5xy)0≠ 0

  16. (5a)-1 = (b)-n = Negative Exponents 8-2 Negative exponents “move” up or down to make it a positive exp. (5a)-1≠ -5a

  17. Negative exponent rule: a-n = a-n is the reciprocal of an Example1: 1. x-3 2. 5a-2b03. -4a-7b-3

  18. Your Turn 1: a. 3w-3 b. 4x-7c. 3x0y-4

  19. Example 2: 4. 5.

  20. Your Turn 2: d. e. f.

  21. Learning target(s): • I can multiply and divide monomials. (LT1) Mixed practice: Simplify expressions means to write expressions without parentheses or negative exponents. a. b. c.

  22. Learning target(s): • I can multiply and divide monomials. (LT1) Mixed practice: d. e. f.

  23. Learning targets: • I can multiply and divide monomials. (LT1) Mixed practice: g. h.

  24. Learning target(s): • I can multiply and divide monomials. (LT1) Mixed practice: Simplify expressions means to write expressions without parentheses or negative exponents. a. b. c.

  25. Learning target(s): • I can multiply and divide monomials. (LT1) Mixed practice: d. e. f.

  26. Learning targets: • I can multiply and divide monomials. (LT1) Mixed practice: g. h.

  27. Homework: Lesson 5.1B

  28. Warm- up over Lesson 5.1A & B Simplify the following. 1. 2. 3. 4. 5. 6.Write a problem involving operations with powers whose answer is: -8x3

  29. 5.1B

  30. Lesson 5.2 (LT3) • I can recognize a monomial, binomial, or trinomial. • I can identify the degree of a polynomial. • I can rewrite polynomials in descending order. • I can add polynomials. • I can subtract polynomials. • I can multiply polynomials.

  31. Definition of monomial

  32. Classify as monomial ornon-monomial Example 1a: Examples: Non Examples:

  33. Definition of Polynomials

  34. Example 1b: Classify as polynomial ornon-polynomial Examples: Non Examples: 51

  35. Your Turn 1: Is it a polynomial? Yes or No? Classify as monomial, binomial, or trinomial? a. 2x3 + 4x2 4 b. 2xy3 – 4x4y0 + 2x c. x2 + 3xy y d. 4x-2

  36. Example 2:Arrange the terms of the polynomial so that the powers of x are in descending order Descending: decreasing (biggest to smallest) a. 4x2 + 7x3 + 5x b. 9x3y – 4x5 + 8y - 6xy4 Your turn 2: c. 10 + 7x3y – 2x4y2 + 8x

  37. Example 3:Find the degree of the monomial. Degreeof a monomial: sum of the exponents of the variables a. 5x2 b. -9x3y5 Your Turn 3: c. 7xy5z4 d. 10

  38. Example 4:Find the degree of the polynomial. Degree of a polynomial: it is the highest degree after finding the degree of each term. a. 5x4+ 3x2 – 9x Your Turn 4: b. 4x3 – 7x + 5x6

  39. Check for Understanding Lesson 5.2 A: (LT3) Is the polynomial a monomial, binomial, or trinomial. a. y3 – 4 b. 3y3 + y0 – 2x c. -4xy5 Arrange the terms of the polynomial so that the powers of x are in descending order. d. 3x4y3 – x6y0 + 6 – 2x Find the degree of the monomial e. -2x4y3z f. 3ab0y3 Find the degree of the polynomial. g. 3x4y3 – x6y0 + 6 – 2x

  40. Example 5: Simplify the following 1. (x2 – 5x + 3) + (2x2 + 4x – 5) 2. (5y2 – 3y + 8) + (4y2 – 9) Your Turn 5: Simplify the following (LT4) (3x2 – 4x + 8) + (2x -7x2 -5)

  41. Example 6: Simplify the following 3. (2x2 – 3x + 1) – (x2 + 2x – 4) 4. (4y2 – 9) – (5y2 – 3y + 8) Your Turn 6: Simplify the following (LT4) (3x2 – 4x + 8) – (2x -7x2 -5)

  42. Example 7:Simplify the following. 1. y( 7y + 9y2) 2. -3x(2x2 + xy – 3)

  43. Your Turn 7:Simplify the following. 1. n2(3n2 + 7) 2. n2(3n2p - np + 7p)

  44. Example 8:Multiply the following. 1. (x + 3)(x + 2) 2. (x  9)(3x + 7) 3.

  45. Your Turn 8: Find the product. (LT5) a. b.

  46. Simplify. c. d. e.

  47. Homework: Practice 5.2

More Related