FANTASTIC FACTORING!!!
This presentation is to be used for educational purposes only.
Greatest Common Factor
Difference of Squares
Perfect Square Trinomial
Leading Coefficient of One
Leading Coefficient Not One
All Five Types
Appendices
Teacher’s Guide
Don’t let
factoring blow
you away!
EXIT
TEACHER’S GUIDE
Introduction
Subject Matter
Aim
Goals and Objectives
Rationale
Instructional Plan
Learners
Materials
Prerequisites
Assessment
Introduction
 Factoring…students often find it hard to learn
and teachers often find it hard to teach!
Students wonder how they can factor
polynomials when each one seems to be a
different style than the last. Teachers wonder
how they can find enough time to teach it
thoroughly when they have so many other
topics to cover.
Aim
 The purpose of this curriculum web is to
provide a resource for students and teachers
where students can learn and practice
factoring the most common types of
binomials and trinomials.
Rationale

Factoring is often one of the mathematical
skills that students find the most difficult to
learn, along with graphing and proofs.
Factoring can also be a source of frustration
for teachers who think students should be
learning the concepts faster or who find
themselves re-teaching factoring in courses
they feel they should not have to spend time
doing.
Rationale Continued…

Sometimes students wonder why they have to
learn factoring. There are at least four reasons
learning to factor polynomials is important.

First, factoring is a skill that is needed to
simplify rational expressions, locate holes in
graphs, and decompose fractions. It can be
used to solve some quadratic equations.
Rationale Continued…

Second, factoring is found throughout the high
school math curriculum. Factoring occurs in
Geometry and Precalculus but factoring is found
predominantly in Algebra I and Algebra II.

Third, as students practice these factoring skills,
they will also practice the very important
algebraic skill of multiplying polynomials which
involves other fundamental skills such as working
with exponents, combining like terms, and
multiplying positive and negative numbers.
Rationale Continued…

Fourth, factoring and skills used in factoring
are among the academic standards for state
testing. For example, the Ohio Academic
Content Standards for Mathematics lists three
educational objectives covered by factoring:
“Solve quadratic equations…by factoring,”
“Add, subtract, multiply and divide monomials
and polynomials…” and “Simplify rational
expressions by eliminating common factors…”
Rationale Continued…

This curriculum web can be a resource
for teachers to provide for their students
when they do not have the personal time
to review how to factor the five different
types of polynomials presented. It can
also be a resource parents can provide
their children who are struggling with
factoring. It can even be a resource for
parents themselves to learn factoring and
explain it to their children.
Rationale Continued…

This curriculum web can enable students
to realize that most factoring problems
are not unique but fall into general
categories. Students can realize that
factoring polynomials does employ
algorithms (step-by-step procedures to
solve them). Lastly, students can
overcome their fear of failure, start to
succeed at factoring, and gain confidence
in approaching factoring problems.
Learners
 This curriculum web is designed to be used
by high school students who have previously
been taught how to factor binomials and
trinomials. Although it could be used to
initially learn how to factor, it is designed to
provide explanations and practice for those
who have been exposed to factoring.
Prerequisites
 Currently taking Algebra I or higher
 Previous exposure to factoring binomials and
trinomials
 Interest in learning more details about
factoring and practicing different problem
styles
Subject Matter
 Algebra I and II
 Factoring binomials and trinomials
 Multiplying polynomials to check factoring
Goals and Objectives
 Students will learn to factor five different
styles of polynomials:
 Greatest Common Factor
 Difference of Squares
 Perfect Square Trinomial
 Trinomials with a leading coefficient of one
 Trinomials with a leading coefficient of an
integer other than one
Instructional Plan

This curriculum web is designed to be used by
students without the help of a teacher. Students
can access the curriculum web and follow the
instructions. Students will find:
Detailed explanations of problems
 Practice quizzes on each factoring style
 Helpful resources for further exploration

Materials
 An Internet-linked computer and web
browser
 Paper and pencil to perform calculations and
check work before submitting answers
 Hand-held calculator is optional and online
calculator links are provided
Assessment
 Learning that occurs through this curriculum
web can be assessed by the online quizzes that
can be taken and the results e-mailed to the
teacher, parent, or student.
 Students can do a self-assessment by using a
rubric to examine their improving skill level.
 EVALUATION: The curriculum web itself can
be evaluated by using a link to a feedback
form in the Appendices.
Appendices

Resources
Ask Dr. Math
 Does the CAREER I want use MATH?!
 More Factoring Practice




Leading Coefficient of One
Leading Coefficient Not One
Online Calculator
Appendices

Glossary (in your language!)

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Binomial – two terms
Coefficient – number in front of the letter
Degree - highest exponent
Factoring – factors that can be multiplied to get
the original problem
Greatest Common Factor – what all the terms
have in common
Perfect Square – has the same two factors
Trinomial – three terms
Appendices
Have you ever used a product and had an idea
you KNOW would make it better? Well here’s
your chance to make your voice heard! (Fill
out this short and simple four-question
evaluation.)
EVALUATION
Fantastic
Factoring
Greatest
Common
Factor
Difference
Of
Squares
Perfect
Square
Trinomial
Leading
Coefficient
of One
Leading
Coefficient
Not One
All
Five
Types
Explanation
Explanation
Explanation
Explanation
Explanation
Online
Practice
Quizzes
Online
Practice
Quizzes
Online
Practice
Quizzes
Online
Practice
Quizzes
Online
Practice
Quizzes
Appendices
Online
Practice
Website
Teacher’s
Guide
Resources
Glossary
Evaluation
Teacher’s Guide
Introduction
Aim
Rationale
Learners
Prerequisites
Subject Matter
Goals and Objectives
Instructional Plan
Materials
Assessment
Appendices
If you would like to see if your factoring skills
are improving you can click on the link below to
rank yourself on a scale from 0 to 5.
SELF-ASSESSMENT
GREATEST COMMON FACTOR
Detailed
Example
Practice Quizzes
Easier than
facing a
300 lb
GORILLA!
DIFFERENCE OF SQUARES
Detailed
Example
Practice Quizzes
Go for
the
GOLD!!!
PERFECT SQUARE TRINOMIAL
Detailed
Example
Practice Quizzes
I love
trinomials!!!
LEADING COEFFICIENT
OF ONE
Detailed
Example
Practice Quizzes
Your
future’s so
bright you
have to
wear
shades!!!
LEADING COEFFICIENT
NOT ONE
Detailed
Example
Practices Quizzes
Come on
sleepy
head!!!
ALL FIVE TYPES
Practice Quizzes
Don’t be a
chicken!!!
Greatest Common Factor

Factor 3ty3 + 36ty2
– Largest number that goes into 3 and 36? Answer: 3
– Highest power of t in both? Answer: t
– Highest power of y in both? Answer: y2

Overall Answer: 3ty2 (y + 12)
Difference of Squares

Factor x2 – 36
– What times what would equal x2? Answer: x
– What times what would equal 36? Answer: 6
– Put x and 6 together, one with a plus and one with
a minus.

Final answer: (x + 6)(x - 6)
Perfect Square Trinomial

Factor x2 – 10x + 25
– What times what would equal x2? Answer: x
– What times what would equal 25? Answer: 5
– Put x and 5 together using the same signs as the
negative 10x.

Final Answer: (x - 5)(x - 5)
Leading Coefficient of One

Factor x2 - 2x - 48
– List factors of 48. Answer: 1&48, 2&24, 4&12,
6&8
– Choose pair that gets 2. Answer: 6&8
– Get signs from - 48. Answer: one + and one –
– Put bigger number with the same sign as middle
term of - 2x

Final Answer: (x – 8)(x + 6)
Leading Coefficient Not One

Factor 8x2 - 46x + 30
– Find 8 times 30. Answer: 240
– List factors of 240. Answer: 1&240, 2&120,
3&80, 4&60, 5&48, 6&40, 8&30, 12&20
– Choose the pair that gets 46. Answer: 6&40
– Write - 46x as - 6x and - 40x.
 Answer: 8x2 - 40x - 6x + 30
– Continued on next page…
Leading Coefficient Not One

Problem Continued…
> 8x2 - 40x - 6x + 30
> Factor first two terms. Answer: 8x (x – 5)
> Factor last two terms. Answer: - 6 (x – 5)
> Put 8x and - 6 together. Answer (8x – 6)
> Write (x – 5) only once.

Overall Answer: (8x – 6)(x – 5)
Thanks for using FANTASTIC
FACTORING!