Factoring Algebra Chapter 8B Assignment Sheet


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1 Name: Factoring Algebra Chapter 8B Assignment Sheet Date Section Learning Targets Assignment Tues 2/17 Find the prime factorization of an integer Find the greatest common factor (GCF) for a set of monomials. Worksheet #1 Wed 2/18 Thurs 2/19 Fri 2/20 Mon 2/23 Tues 2/24 Wed 2/25 Thurs 2/26 Fri 2/27 Mon 3/2 Tues 3/3 Wed 3/4 Thurs 3/5 Fri 3/6 8.2 Use GCF and distributive property to factor polynomials Pg 494 #3, 4, 1526, Use grouping techniques to factor polynomials with four or more terms This is an outline. The assignments/quizzes/tests are subject to change. Pg 531 #1, 2, 1316, 18, 19, Factoring quadratic trinomials (leading coefficient of 1) Worksheet #4 8.6 Factoring quadratic trinomials (leading coefficient not 1) Quiz Day 1, 8.2, 8.8 Pg 520 #13, 819 S8.5 & S8.6 Review Worksheet #6 S8.5 & S8.6 Review Quiz Day 1, 8.2, 8.8, 8.5, Factor polynomials that are the difference of squares Pg 526 #3, 7, Factor perfect square trinomials Pg 526 #1, 2, 920 Worksheet #7 Factor polynomials requiring more than one step Worksheet #10 CLS Testing Day Worksheet #11 Chapter 8B Review Quiz Chapter 8B (all sections) Chapter 8B Review Chapter 8B Test Worksheet #12 Practice Test
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3 Algebra Ch 8B Factoring PreAlgebra Review Factors and Greatest Common Factors Name Learning Targets: Students will be able to: find the prime factorization of an integer, and find the greatest common factor (GCF) for a set of monomials. Prime Number Composite Number A whole number, greater than 1, whose only factors are 1 and itself. A whole number, greater than 1, that is not prime. Greatest Common Factor The product of the prime factors common to the integers. EXAMPLES Ex 1) Find the prime factorization of each number. a. 200 b. 650 c. 420 d. 168 Ex 2) Factor. a b. 448
4 Ex 3) Factor. a. 45a 2 b 2 b. 77ab 2 Ex 4) Find the GCF of the following. a. 40 and 60 b. 64 and 80 Ex 5) Find the GCF of the following. a. 40a 2 b and 48ab 4 b. 18x 3 and 6x ASSIGNMENT #1: Worksheet
5 Algebra Ch 8B Factoring Section 8.2 Factoring Using the Distributive Property Name WARM UP: Find the GCF of the given monomials. 1) 4xy, 6x 2) 60x 2 y 2, 35xz 3 Learning Target: Students will be able to use the GCF and the distributive property to factor polynomials. Recall the Distributive Property a b c ab ac Multiplying Polynomials 3 a b x y z 3y 4x 2 Factoring Polynomials 3a 3b xy xz 12xy 6y EXAMPLES: Factor a 4 15a x 2 12x y y y 4. 28a 2 b 56abc xy 2 24y 2 z 40y ab ab a b ASSIGNMENT#2: Pg 494 #3, 4, 1526, 3739
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7 Algebra Ch 8B Factoring Section 8.8 Factoring by Grouping Name Learning Target: Students will be able to use grouping techniques to factor polynomials with four or more terms. Steps to factor by grouping: o Group (put parenthesis) around the first two and second two terms. CAUTION! DO NOT separate any term from its sign with these parenthesis! o Factor the GCF from each pair. o Notice the common binomial factor (if there isn t one, rearrange the terms and go back to step 1). o Factor the common binomial from each term and leave the leftovers as the other binomial. o Answer will be the PRODUCT of two binomials. FOIL to check. Ex 1) 10m 2 n 25mn 6m 15 Ex 2) 2 16a b 24ab 2a 3 Ex 3) 20ab 35b 63 36a Ex 4) 3x 3 2xy 15x 2 10y Ex 5) a 2 ab 7b 7a Ex 6) 3a 2 2ab 10b 15a ASSIGNMENT #3: Pg 531 #1, 2, 1316, 18, 19, 21
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9 Algebra Ch 8B Factoring Section 8.5 Factoring Trinomials Name WARM UP: Complete the table below by finding the two numbers that give each product and sum. Product Sum Factors Learning Target: Students will be able to factor quadratic trinomials with a leading coefficient of 1. FOIL the following: x 3 x 9 Factor the following: x 2 12x 27 When the coefficient of the highest degree term is 1, we will use what I call the PUZZLE METHOD. Here we solve the puzzle of finding two numbers that MULTIPLY to get the LAST term and ADD to get the MIDDLE term. We then use those numbers in our binomials and FOIL to check. Ex 1) a 2 22a 21 Ex 2) b 2 12b 35 Ex 3) x 2 5x 24 Ex 4) c 2 2c 3 Note: If the problem cannot factor, we write PRIME as the answer. There will be very few PRIME problems given in this chapter, but every once in a while one appears. ASSIGNMENT #4: Worksheet
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12 Algebra Ch 8B Factoring Section 8.6 Factoring Trinomials Name WARM UP: Factor 1) x 2 10x 21 2) x 2 x 6 3) x 2 5x 6 Learning Target: Students will be able to factor quadratic trinomials with a leading coefficient NOT 1. When the coefficient of the highest degree term is NOT 1, we will use GUESS and CHECK. GUESS terms to use in our binomials that multiply to get our first terms and our last terms and then FOIL to CHECK if it works. Certain problems can be frustrating at times due to all of the choices, but keep with it and don t give up! Ex 1) 2x 2 9x 10 Ex 2) 3a 2 13a 4 Ex 3) 15x 2 13x 2 Ex 4) 8a 2 14a 3 Ex 5) 6y 2 13y 5 Ex 6) 12x 2 11x 5 ASSIGNMENT #5: Pg 520 #13, 819 ASSIGNMENT #6: Worksheet ASSIGNMENT #7: Worksheet
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14 Algebra Ch 8B Factoring Section 8.7 WARM UP: Factor. 1) y 2 15y 56 Difference of Squares and Factoring 2) 10x 2 9x 9 Name Learning Target: Students will be able to identify and factor polynomials that are the difference of squares. Recall from Chapter 6: Product of a Sum and a Difference a b a b a 2 b 2 x 5 x 5 New: Difference of Squares Sum of Squares a 2 b 2 a b a b a 2 b 2 PRIME!!! x 2 25 EXAMPLES: Factor completely. Ex 1) x Ex 2) 16x 2 25y 2 Ex 3) a 2 9 ***Caution Ex 4) 81a 2 16y 2 Ex 5) 25x 2 1 Ex 6) 36p 2 49q 2 ASSIGNMENT #8: Pg 526 #3, 7, 2435
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16 Algebra Ch 8B Factoring Section 8.7 Perfect Squares and Factoring Name WARM UP: Factor. 1) n ) 25a 2 100b a 2 1 Learning Target: Students will be able to identify and factor perfect square trinomials. Recall from Chapter 6: New: Square of a Sum/Difference Perfect Square Trinomials a b 2 a 2 2ab b 2 a b 2 a 2 2ab b 2 2 a 2 2ab b 2 a b a 2 2ab b 2 a b 2 Examples: Determine whether each of the following is a perfect square. If it is, factor it. Ask yourself: 1. Is the first term a perfect square? 2. Is the last term a perfect square? 3. Is the middle term two times the product of the square root of the first and square root of the last term? Ex 1) x 2 12x 36 Ex 2) a 2 14a 49
17 Ex 3) 49v 2 56v 16 Ex 4) 25t 2 30t 36 Ex 5) 49 25t 2 70t ASSIGNMENT #9: Page 526 #1, 2, 920
18 Algebra Ch 8B Factoring Name MultiStep Factoring WARM UP: Factor. 1) n 2 14n 49 2) 9t 2 42tv 49v 2 Learning Target: Students will be able to factor polynomials by applying the various methods of factoring. *LET S LOOK AT THE FACTORING FLOW CHART TO COMPLETE THE FOLLOWING EXAMPLES* EXAMPLES: Factor completely Ex 1) 2n 2 10n 72 Ex 2) 75x 2 60xy 12y 2 Ex 3) 3x 2 48 Ex 4) 75a 4 12a 2 Ex 5) 12y 2 32y 20 Ex 6) a 4 81 ASSIGNMENT #10: Worksheet ASSIGNMENT #11: Worksheet
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