Factoring Algebra- Chapter 8B Assignment Sheet

“Factoring”

Algebra- Chapter 8B Assignment Sheet

This is an outline. The assignments/quizzes/tests are subject to change.

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

8.2

 Use GCF and distributive property to factor polynomials Pg 494

#3, 4, 15-26, 37-39

Thurs

2/19

8.8

 Use grouping techniques to factor polynomials with four or more terms

Pg 531

#1, 2, 13-16, 18, 19, 21

Fri

2/20

8.5

 Factoring quadratic trinomials (leading coefficient of 1) Worksheet #4

Mon

2/23

8.6

 Factoring quadratic trinomials (leading coefficient not 1) Quiz Day 1, 8.2, 8.8

Pg 520 #1-3, 8-19

Tues

2/24

S8.5 & S8.6 Review Worksheet #6

Wed

2/25

S8.5 & S8.6 Review Quiz Day 1, 8.2, 8.8, 8.5, 8.6 Worksheet #7

Thurs

2/26

8.7

 Factor polynomials that are the difference of squares Pg 526 #3, 7, 24-35

Fri

2/27

8.7

 Factor perfect square trinomials Pg 526

#1, 2, 9-20

Mon

3/2

 Factor polynomials requiring more than one step Worksheet #10

Tues

3/3

CLS Testing Day Worksheet #11

Wed

3/4

Chapter 8B Review Quiz Chapter 8B (all sections)

Worksheet #12

Thurs

3/5

Chapter 8B Review Practice Test

Fri

3/6

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 d. 168

Ex 2) Factor.

Ex 3) Factor.

a. _45a2b2 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. 40a2b and 48ab4 _{b. 18x}3 and

_6x

Factoring Using the Distributive Property

WARM UP: Find the GCF of the given monomials.

1) _4xy,6x _{2) 60x}2y2, 35xz3

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 Factoring Polynomials

3 a

 

b  3a3b x y

 

z  xyxz 3y 4x



2



 12xy6y EXAMPLES: Factor. 1. _25a415a2 2.. _18x2 12x3 3. 3 2 8y 4y 2y

4. 28a2b56abc2 _{5. 16xy}224 y2z40 y2 6. 17ab351ab34a b2

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) _10m2n25mn6m15 Ex 2) 16a b2 24ab2a3

Ex 3) _20ab35b6336a _{Ex 4) 3x}32xy15x210 y

Ex 5) _a2 ab7b7a Ex 6) _3a22ab10b15a

Factoring Trinomials

WARM UP: Complete the table below by finding the two numbers that give each product and sum.

Product Sum Factors

20 9 15 -8 -12 1 18 9 25 -10 -14 5 45 -14

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) _x2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.

Algebra Name_____________________ Ch 8B Factoring

Section 8.6

Factoring Trinomials

WARM UP: Factor

1) x2 10x21 2) x2 x 6 3) x2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) 2x2 9x10 _{Ex 2) 3a}2  13a4 Ex 3) _15x213x2 Ex 4) _8a214a3 Ex 5) 6y2 13y5 Ex 6) _12x211x5 ASSIGNMENT #5: Pg 520 #1-3, 8-19 ASSIGNMENT #6: Worksheet ASSIGNMENT #7: Worksheet

Algebra Name_____________________ Ch 8B Factoring

Section 8.7

Difference of Squares and Factoring

WARM UP: Factor.

1) 2

15 56

y  y 2) _10x2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 2  b2

 

x5

 

x5  New: Difference of Squares a 2 b2 

 

ab

 

ab _x225

Sum of Squares _a2b2 PRIME!!!

EXAMPLES: Factor completely.

Ex 1) _x2121 _{Ex 2) 16x}225y2

Ex 3) _a2

9 ***Caution _{Ex 4) 81a}2 16 y2

Ex 5) _25x2 1 _{Ex 6) 36p}249q2

Algebra Name_____________________ Ch 8B Factoring

Section 8.7

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: Square of a Sum/Difference

 

ab 2 a22abb2

 

ab 2 a22abb2

New: Perfect Square Trinomials

a 2 2abb2 

 

ab 2 a 2 2abb2 

 

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 5) ₄₉25t270t

Algebra Name_____________________ Ch 8B Factoring

Multi-Step Factoring

WARM UP: Factor.

1) _n214n49 2) _9t242tv49v2

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12 y2

Ex 3) _3x248 Ex 4) _75a412a2

Ex 5) 12y232 y20 Ex 6) a481

ASSIGNMENT #10: Worksheet ASSIGNMENT #11: Worksheet