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Warm-Up 3/23 What is the area and perimeter of a rectangle in simplest form if the side lengths are 3x – 4 and 2x + 1? Warm-Up 3/23 Prime numbers –whole numbers that have exactly two factors, 1 and itself. Using the above definition, list as many prime numbers as you can starting with 1. 1, __ , __ , __ , __ , __ , __ , Opening Watch Video: Finding the GCF http://www.phschool.com/atschool/academy12 3/english/academy123_content/wl-bookdemo/ph-877s.html Warm-Up 3/24 A rental car costs $150 a week, plus $0.10 per mile. Which equation represents the relationship between the number of miles, x, and the total cost in dollars, y, for a two week rental? A.5.C (R) A. y = 150 + 2(0.10x) B. y = 2(150)(0.10x) C. y = 2(150 + 0.10x) D. y = 2(150) + 0.10x Opening List all factors of 12. List all factors of 36. What would be the GCF between 12 and 36? Opening Use Prime Factorization to find the GCF of… 1. 18 24 2. 72ab 36b Now Try… 3. 32x3 96xy2 Work Time Find the GCF: 1. 100ab 50ab2 2. 28x2y 35xy 3. 64x5 24x3 Work Time Find the GCF: 1. 100ab 50ab2 2. 28x2y 35xy 3. 64x5 24x3 Closing Show 2 or 3 different ways to factor: 64x5 24x3 64x5 24x3 From Yesterday… Find the GCF:- Check your answers from yesterday. 1. 100ab 50ab2 - GCF = 50ab 2. 28x2y 35xy - GCF = 7xy 3. 64x5 24x3 - GCF = 8x3 Warm-Up 3/19 Find the GCF of the 3 terms: 4x 6 6x 4 10x 2 Factoring with the GCF Work Backwards: 2x2 ? ? 4x6 6x4 ? 10x2 Factoring with the GCF Work Backwards: ? 3x2 9x4 ? 18x3 ? 3x2 Factoring with the GCF Work Backwards: ? 4p 20p3 ? 16p2 ? -12p 3.Factoring Factoringwith Polynomials the GCF Work Backwards: 2x4 ? ? 16x8 14x7 ? 4x6 ? 10x4 3.Factoring Factoringwith Polynomials the GCF Work Backwards: ? 2x2y 4x6y3 ? 10x3y4 ? 6x2y Factoring with the GCF Work Backwards: ? 6x3y2 12x8y3 ? 18x3y4 ? 6x4y2 Factoring with the GCF Find GCF: 4x GCF: Now Factor: (4x + 12) 12 3. Factoring FactoringPolynomialswith the GCFGCF Find the GCF of these 3 terms: 9x2 12x GCF: Now Factor: (9x2 + 12x – 6) -6 3. Factoring PolynomialsGCF Exit Ticket Now Factor: 2 (9m + 5m) Exit Ticket Now Factor: (10w3 + 10w2) Warm-Up 3/20 Factor the following trinomial: 4 40y + 3 20y – 60y Objective: Students will find the factors of trinomials by using the box method. Opening: Factor the Trinomial x x2 4x + 2 2x 8 Trinomial: Factors: How are 4 and 2 related to the 2nd and 3rd term? Opening: Factor the Trinomial 3.) Factor the Trinomial 2 x 3x 2x 6 Trinomial: Factors: How are 3 and 2 related to the 2nd and 3rd term? Work Factor the Trinomial 3.)Time: Factor the Trinomial 2 x 2x 5x 10 Trinomial: Factors: How are 5 and 2 related to the 2nd and 3rd term? Work Factor the Trinomial 3.)Time: Factor the Trinomial 2 x -3x -3x 9 Trinomial: Factors: How are -3 and -3 related to the 2nd and 3rd term? Work Factor the Trinomial 3.)Time: Factor the Trinomial 2 x -3x -12 Trinomial: Factors: How can we find that empty square? Work the Trinomial 3.)Time: FactorFactor the Trinomial 2 x -8x 72 Trinomial: Factors: How can we find that empty square? ofTrinomial the Day 3.) Question Factor the How does knowing the sum and product of specific numbers help you to find the factors of a trinomial? Teach: Factor the Trinomial 2 x 10 ( )( )= 2 x + 11x + 10 Teach: Factor the Trinomial 2 x 24 ( )( )= 2 x – 11x + 24 Work Time: Factor the Trinomial ( )( )= 2 x + 10x + 25 Close: Factor the Trinomial ( )( )= 2 x – 1x – 42 Warm-Up 3/21 Think of 2 numbers that multiply to be the top number and add to be the bottom number. Opening How do you know if you need to factor out the GCF or factor using the box method? Example x2 + 7x + 12 8x3 + 4x2 + x Work Time Students will practice factoring with GCF and by box. Closing Pick a problem that was a challenge. Warm-Up 3/22 Factor the trinomial: 2 x + 14x + 24 Opening 3/22 What happens when the coefficient of x2 is not 1? Example: 2x2 + 7x – 9 Opening 3/22 What happens when the coefficient of x2 is not 1? Example: 3x2 + 8x + 4 Work Time 3/22 Students factor when a > 1. Closing 3/22 Pick 1 or 2 problems to share. Warm-Up 3/25 Factor the trinomial: 2 x – 11x + 30 Opening 3/25 Factor the trinomial: 2 2x + 8x – 10 Difference of Squares Now Factor: x2 – 36 2 x ? ? -36 Difference of Squares Factor: 1. 2. 3. 4. 5. (x2 – 16) = (x2 – 25) = (x2 – 100) = (x2 – 144) = (x2 + 4) = Check: Work Time Practice when a = 1, a > 1, and difference of squares. Exit Ticket 5. Given the following rectangle with area of x2 – 36, what are possible dimensions for the length and width ? X2 – 36 Which of these dimensions are possible side lengths? I (x + 6) A. I and IV C. II only II (x – 6) III (x – 1) B. I and II D. I, II, III, IV IV (x + 36) Warm-Up 3/26 Factor the trinomial: 2 4x + 3x – 10 Work Time Quiz Warm-Up 3/27 Which value of c makes the 2 expression x + 10x + c 2 factor to (x + 5) ?