Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name:__________________ “Factoring” Algebra- Chapter 8B Assignment Sheet Date Section Learning Targets Find the prime factorization of an integer Find the greatest common factor (GCF) for a set of monomials. NO SCHOOL NO SCHOOL 8.5 Factoring quadratic trinomials (leading coefficient of 1) Worksheet #2 8.6 Factoring quadratic trinomials (leading coefficient not 1) Assignment #3: Pg 520 #1-3, 8-19 Quiz S8.5 & S8.6 Review Worksheet #4 S8.5 & S8.6 Review (Pep Assembly Schedule) Worksheet #5 8.2 Use GCF and distributive property to factor polynomials Assignment #6: Pg 494 #3, 4, 15-26, 37-39 8.8 Use grouping techniques to factor polynomials with four or more terms Assignment #7: Pg 531 #1, 2, 13-16, 18, 19, 21 Worksheet #8 Fri 2/12 Mon 2/15 Tues 2/16 Wed 2/17 Thurs 2/18 Fri 2/19 Mon 2/22 Tues 2/23 Wed 2/24 Thurs 2/25 Fri 2/26 Mon 2/29 Tues 3/1 Wed 3/2 Thurs 3/3 Fri 2/26 Assignment Worksheet #1 Quiz S8.2 & S8.8 Review 8.7 Factor polynomials that are the difference of squares Assignment #9: Pg 526 #3, 7, 24-35 8.7 Factor perfect square trinomials Assignment #10: Pg 526 #1, 2, 9-20 Factor polynomials requiring more than one step Worksheet #11 Quiz Chapter 8B Review Worksheet #12 Chapter 8B Review Worksheet #13 Chapter 8B Review Practice Test Chapter 8B Test This is an outline. The assignments/quizzes/tests are subject to change. Algebra Ch 8B Factoring Pre-Algebra Review Name_____________________ Factors and Greatest Common Factors 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 A whole number, greater than 1, whose only factors are 1 and itself. Composite Number 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 Ex 2) Factor. a. -210 b. -448 d. 168 Ex 3) Factor. a. 45a 2b2 b. 77ab2 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 2b and 48ab4 ASSIGNMENT #1: Worksheet b. 18x 3 and 6x Algebra Ch 8B Factoring Section 8.5 Name_____________________ Factoring Trinomials WARM UP: Complete the table below by finding the two numbers that give each product and sum. Product Sum 20 9 15 -8 -12 1 18 9 25 -10 -14 5 45 -14 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) a2 22a 21 Ex 2) b2 12b 35 Ex 3) x 2 5x 24 Ex 4) c2 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 #2: Worksheet Algebra Ch 8B Factoring Section 8.6 Name_____________________ Factoring Trinomials WARM UP: Factor 1) x2 10 x 21 3) x2 5x 6 2) x2 x 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) 3a2 13a 4 Ex 3) 15x 2 13x 2 Ex 4) 8a2 14a 3 Ex 5) 6 y 2 13y 5 Ex 6) 12x 2 11x 5 ASSIGNMENT #3: Pg 520 #1-3, 8-19 ASSIGNMENT #4: Worksheet ASSIGNMENT #5: Worksheet Algebra Ch 8B Factoring Section 8.2 Name_____________________ Factoring Using the Distributive Property 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 ab Factoring Polynomials 3a 3b x y z 3y 4x 2 xy xz 12xy 6y EXAMPLES: Factor. 1. 25a4 15a2 2.. 18x 2 12x3 3. 8 y3 4 y 2 2 y 4. 28a2b 56abc2 5. 16xy 2 24y 2 z 40y 2 6. 17ab3 51ab 34a2b ASSIGNMENT#6: Pg 494 #3, 4, 15-26, 37-39 Algebra Ch 8B Factoring Section 8.8 Name_____________________ Factoring by Grouping 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) 10m2 n 25mn 6m 15 Ex 2) 20ab 35b 36a 63 Ex 3) 16a2b 24ab 2a 3 Ex 4) 3x3 2xy 15x 2 10y Ex 5) a2 ab 7b 7a Ex 6) 3a2 2ab 10b 15a ASSIGNMENT #7: Pg 531 #1, 2, 13-16, 18, 19, 21 ASSIGNMENT #8: Worksheet Algebra Ch 8B Factoring Section 8.7 Name_____________________ Difference of Squares and Factoring WARM UP: Factor. 1) y 2 15 y 56 2) 10x 2 9x 9 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 ba b a New: Difference of Squares a2 b2 a b a b Sum of Squares a2 b2 PRIME!!! 2 b2 EXAMPLES: Factor completely. Ex 1) x 2 121 Ex 2) 16x 2 25y 2 Ex 3) a 2 9 ***Caution Ex 4) 81a 2 16 y 2 Ex 5) 25x 2 1 Ex 6) 36 p2 49q2 ASSIGNMENT #9: Pg 526 #3, 7, 24-35 x 5x 5 x 2 25 Algebra Ch 8B Factoring Section 8.7 Name_____________________ Perfect Squares and Factoring WARM UP: Factor. 1) n2 81 2) 25a2 100b2 3. 36a2 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 a a b a 2 2 2ab b2 2 2 2ab b2 a b a2 2ab b2 a b 2 a2 2ab b2 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) a2 14a 49 Ex 3) 49v 2 56v 16 Ex 5) 49 25t 2 70t ASSIGNMENT #10: Page 526 #1, 2, 9-20 Ex 4) 25t 2 30t 36 Algebra Ch 8B Factoring Name_____________________ Multi-Step Factoring WARM UP: Factor. 1) n2 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) 2n2 10n 72 Ex 2) 75x 2 60xy 12y 2 Ex 3) 3x 2 48 Ex 4) 75a4 12a2 Ex 5) 12y 2 32y 20 Ex 6) a 4 81 ASSIGNMENT #11: Worksheet ASSIGNMENT #12: Worksheet