Math 8_ Week 1 - Greatest Common Monomial Factor.pptx.pdf

MATHEMATICS 8 1st quarter: week 1 SPECIAL PRODUCTS AND FACTORING  SPECIAL PRODUCTS The process of finding products of binomials using short methods. Some special products are a) Square of a Binomial b) Cube of a Binomial c) Product of a Sum and Difference ...

MATHEMATICS 8 1st quarter: week 1 SPECIAL PRODUCTS AND FACTORING  SPECIAL PRODUCTS The process of finding products of binomials using short methods. Some special products are a) Square of a Binomial b) Cube of a Binomial c) Product of a Sum and Difference  factoring The reverse of finding the related products. Rewriting a polynomial as a product of polynomial factors is called factoring polynomials. a) Difference of Two Squares b) Sum and Difference of Two Cubes c) Factoring Quadratic Trinomials ax2 + bx + c d) Factoring by Grouping OBJECTIVES: -Determine the greatest common monomial factor of a polynomial -Recall how to determine the greatest common factor of whole numbers -Solve problems involving factoring greatest common monomial factors FACTORING POLYNOMIALS  FACTORING Factoring is the process of determining the factors of constants, variables, or combination of constants and variables. There are many ways on how to factor polynomials. The first step is to check if the polynomial has a greatest common monomial factor. Common monomial factor  Review (Greatest Common Factor) Example 1: Listing Method: Find the GCF of 20, 24, 56 20: 1, 2, 4, 5, 10, 20 24: 1, 2, 3, 4, 6, 8, 12, 24 GCF: 4 56: 1, 2, 4, 7, 8, 14, 28, 56  Review (Greatest Common Factor) Continuous Division: Find the GCF of 20, 24, 56 2 20 24 56 2 10 12 28 GCF: 2 x 2 5 6 14 =4  Find the GCF of the ff: 1) 10, 16, 30 2) 15, 27, 54 3) 8, 24, 32 Review (Greatest Common MONOMIAL Factor) Find the GCF of x3y2z3, x4y5z, x2y2z x3y2z3 = x ⋅ x ⋅ x ⋅ y ⋅ y ⋅ z ⋅ z ⋅ z x4y5z = x ⋅ x ⋅ x ⋅ x ⋅ y ⋅ y ⋅ y ⋅ y ⋅ y2⋅ 2z x y z=x⋅x⋅y⋅y⋅z GCF: x ⋅ x ⋅ y ⋅ y ⋅ z = x2y2z Review (Greatest Common MONOMIAL Factor) Find the GCF of x3y2z3, x4y5z, x2y2z x3y2z3 = x ⋅ x ⋅ x ⋅ y ⋅ y ⋅ z ⋅ z ⋅ z x4y5z = x ⋅ x ⋅ x ⋅ x ⋅ y ⋅ y ⋅ y ⋅ y ⋅ y2⋅ 2z x y z=x⋅x⋅y⋅y⋅z GCF: x ⋅ x ⋅ y ⋅ y ⋅ z = x2y2z Find the GCMF of the ff: 1) a4b2, ab4c, a2b3c 2) m3n2o, m2n4, m2n5o Review (Greatest Common MONOMIAL Factor) Find the GCF of 12a2b3c3, 24ab4c, 18a4b2c2 Use the distributive property to complete the following: 1) x2 + 2x x( x + 2 ) 2) 6x3 - 10x2 2x2 ( 3x - 5 ) 3) 4y4z2 + 4yz2 ( y3 + 2z2 ) 8yz4 QUIZIZZ: GCMF More Examples Polynomial GCF Factored Form 1) x2 + 2x x x (x + 2) 2) 4x2 + 6x 3) 5x + 10x2 4) 6x4 - 14x2  FACTOR THE POLYNOMIAL Example 1: 3 2 2 15x y - 10x y 15x3y 15x3y 10x y 2 2 = 5x2y 5x2y 310x ⋅5⋅x⋅x⋅x⋅y⋅ 2 2 y 3x 2y y = Factor Form: 2⋅5⋅x⋅x⋅y⋅ GCF: 5x2y y 2 (5x y) (3x - 2y)  FACTOR THE POLYNOMIAL Example 2: 8a3(x+y)3 + 12a2(x+y)5 8a3(x+y)3 8a3(x+y)3 12a2(x+y)5 12a2(x+y)5 4a2(x+y)3 4a2(x+y)3 GCF: 2 4a (x+y) 3 2a + 3(x+y)2 Factor Form: [4a2][2a + 3(x+y)2]  Find the factors of the ff polynomials: 1) 6x3-5x2+2x 2) 40a3b2c7 - 20a4bc + 100b5c4  Find the factors of the ff polynomials: 3) 6x3y2-10xy3+18x2y 4) 36(a-b)4-18(a-b)7  MATH BOOK (page 7) Answer Practice and Application (Roman Numeral I) numbers 1-9. Announcement (Summative test #1: July 19, 2024) 1. Study the following: Factoring Polynomials with Common Monomial Factor: pages 2-9 Difference of Two Squares: pages 11-14 2. Quiz on Thursday, July 18, 2024. 3. Handouts will be posted through Google Classwork. 4. Please be present on your Quiz day! Announcement (Summative test #1: July 19, 2024) 1. Study the following: Factoring Polynomials with Common Monomial Factor: pages 2-9 Difference of Two Squares: pages 11-14 2. Quiz on Friday, July 19, 2024. 3. Handouts will be posted through Google Classwork. 4. Please be present on your Quiz day! OBJECTIVES: -Recall how to obtain the products resulting in difference of two squares -Determine if the given polynomial is factorable using the difference of two squares -Factor polynomials in the form of difference of two squares difference of two squares Factoring difference of two squares  Review (Multiplying Polynomials) POLYNOMIALS PRODUCT (x + 8) (x - 8) 2 x - 64 (2y + 9) (2y - 9) 4y2 - 81 (a2b2 + 6c) (a2b2 - 6c) a4b4 - 36c2 Factor the following: 2 2 2 1) x - 16y 2) a - 25 2 2 = (x) - (4y) = = (x+4y) (x-4y) = (a + 5)(a-5)  Factor the following: 3) 81a6b4 - 25c8 4) x4 - 16 = (9a3b2)2 - (5c4)2 = (x2)2 - (4)2 2 2 3 2 4 = (x + 4) (x - 4) = (9a b + 5c ) (9a3b2- 5c4) = (x2 + 4) [(x)2 - (2)2] 2 = (x + 4) (x + 2) (x - 2) Factor the following: a2 - b2 9x2 - 49 25a4 - 121b2 Find the factors of the ff polynomials: 1) 81a4-625 2) 36 a6- 144 Seatwork #1: By Pair, ½ Crosswise Factor the following: 1.) 8x3 + 18 x4 -6x6 2.) 12a4 b2- 3ab2 3.) 64x2 - 100 End of presentation