Download “Factoring” Algebra- Chapter 8B Assignment Sheet Fri 2/12 Mon 2

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 ab 
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  ba  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  5x  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