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MATHEMATICS 8 MATATAG QUARTER1 W5 Day1.pptx
- 2. Begin the lesson by recalling the prior knowledge on the concept of area of squares and rectangle with emphasis SHORT REVIEW
- 3. Activity No. 1 – Let’s Investigate FACTORS OF THE AREA OF THE RECTANGLE OR SQUARES ARE THE MEASUREMENT OF ITS DIMENSIONS.
- 6. THE WHOLE NUMBERS THAT ARE MULTIPLIED TO FIND A PRODUCT ARE CALLED FACTORS OF THAT PRODUCT. A NUMBER IS DIVISIBLE BY ITS FACTORS. YOU CAN USE THE FACTORS OF A NUMBER TO WRITE THE NUMBER AS A PRODUCT. THE NUMBER 12 CAN BE FACTORED IN SEVERAL WAYS
- 8. THE ORDER OF THE FACTORS DOES NOT CHANGE THE PRODUCT, BUT THERE IS ONLY ONE EXAMPLE ABOVE THAT CANNOT BE FACTORED FURTHER. THE LAST FACTORIZATION IS THE PRIME FACTORIZATION SINCE ALL THE
- 9. THE PRIME FACTORS CAN BE WRITTEN IN ANY ORDER, AND, EXCEPT FOR CHANGES IN THE ORDER, THERE IS ONLY ONE WAY TO WRITE THE PRIME FACTORIZATION OF A NUMBER.
- 10. FACTOR REFERS TO A NUMBER OR POLYNOMIAL THAT IS MULTIPLIED BY ANOTHER NUMBER OR POLYNOMIAL TO FORM A PRODUCT.
- 11. WHAT DO YOU THINK THE WORD FACTOR MEANS WHEN IT IS USED AS A VERB (ACTION
- 12. List some words that end with the suffixes -ize or - ization.
- 13. What does the ending -ization seem to mean? What do you think factorization means?
- 14. The words prime, primer, primary, and primitive all come from the same root word.
- 15. What are the meanings of these words? How can their meanings help you understand what a prime factor is?
- 16. What is a prime number? How might the prime factorization of a number differ from another factorization?
- 17. What does the word common mean? How can you use this meaning to understand the term greatest common factor?
- 19. Question # 7 a(b + c) = ab + ac
- 20. To understand how to factor out common factors, we must understand the distributive property. For example, we can use the distributive property to find the product of 3x2 and 4x + 3 as shown below
- 21. Notice how each term in the binomial was multiplied by a common factor of 3x2.
- 22. Question # 9 Since the distributive property is an equality, the reverse of this process is also true. The reverse process is called Factoring
- 23. Question # 10 Remember that a polynomial is factored completely when it is expressed as a product of one or more
- 24. Question # 10 Not all polynomials can be factored. To factor a polynomial completely: Identify and factor out the
- 25. • Break down every term into prime factors. • Look for factors that appear in every single term to determine the GCF. • Factor the GCF out from every term in front of parentheses and group the leftovers inside the parentheses. • Multiply each term to simplify.
- 26. EXAMPLE The GCF (greatest common factor) of two or more monomials is the product of all their common prime factors. Let us now try to factor
- 28. STEPS Break down every term into prime factors. Look for factors that appear in every single
- 29. STEPS Term to determine the GCF Factor the GCF out from every term in front of parentheses and group the leftovers inside the parentheses.
- 30. STEPS Multiply each term to simplify
- 35. Use algebra tile to factor the following Directions
- 36. 1.4x2+6x
- 37. STEP S RESUL TS Model the polynomial Arrange the tiles to form rectangle Find the measure of the length and width. Note: The length and width of the rectangles represent the
- 39. 2. y2-4y
- 40. STEP S RESUL TS Model the polynomial Arrange the tiles to form rectangle Find the measure of the length and width. Note: The length and width of the rectangles represent the
- 42. 3.3xy+6
- 43. STEP S RESUL TS Model the polynomial Arrange the tiles to form rectangle Find the measure of the length and width. Note: The length and width of the rectangles represent the
- 45. DIRECTIONS: FACTOR THE FOLLOWING POLYNOMIALS. YOU MAY USE ALGEBRA TILE TO REPRESENT THE FACTORS. PART II: WARM-UP WITH TILES
- 46. 1.2x+10 (______) (______) 2.6x-8 (______) (______) 3.5x2+2x (______) (______) 4.9-3xy (______) (______) 5.y2+2y (______) (______)
- 47. DIRECTIONS: FACTOR THE FOLLOWING POLYNOMIALS FINDING THE COMMON FACTOR. PART III: MORE PRACTICE!
- 48. 1.12a2+16a (______) (______) 2.8cd2+12c2d+9cd (______) (______)
- 49. What you have learned In a one sheet of paper write something you understand about the lesson we discussed
- 50. Directions: Read and answer each question carefully. Show your solution for number 8
- 51. 1. What is the Distributive Property? A. a + b = b + a B. a(b + c) = ab + ac C. a × a = a² D. ab – ac = a(b + c)
- 52. 2. Which expression shows the use of distributive property for 5(x+2)? A. 5x+2 B. 5x+10 C. 5x+2x
- 53. 3. What is the GCF of the terms 4x2 and 6x?? A. 2 B. 4x C. 2x D. 6x
- 54. 4. Which of the following is the factored form of 4x2+6x? A. (2x)(2x+3) B. (4x)(x+2) C. (x)(4x+6)
- 55. 5. Which of the following steps comes first in factoring? A. Multiply each term B. Group terms inside the parentheses C. Break down every term into prime factors
- 56. Write the correct answer on the blank.
- 57. 6.What do we call the number or variable that is common to every
- 58. 7. What property allows you to distribute a factor over terms inside
- 59. Show your solution and write the final
- 60. 8. Use the distributive property to expand:
- 63. ANSWE R
- 64. 1.B 2.B 3.C 4.A 5.C 6. Greatest Common Factor (GCF) 7. Distributive Property
- 65. 8. Solution: 3x(x) + 3x(5) = 3x2 + 15x Answer: 3x2 + 15x 9. Solution: GCF of 12x2 and 16x is 4x
- 66. 10. GCF = 5x = 5x (3x + 2) Answer: 5x (3x + 2)
- 67. Thank You!