Hart Interactive Algebra 2 & Algebra 2/Trig Module 2

214 Pages·2017·2.68 MB·English

Hart Interactive
Algebra 2 & Algebra 2/Trig
Module 2 – Student Workbook

Polynomial, Rational and Radical Relationships
Unit 6: Polynomial Graphs – Lessons 1 – 12
Unit 7: Rational Functions and Their Operations – Lessons 13 - 23

Name: _____________________________
Period: ______
Teacher: ___________________________

Hart Interactive – Algebra II

Mathematics Curriculum
ALGEBRA II • MODULE 2

Table of Contents1
Polynomial, Rational, and Radical
Relationships
Module Overview .................................................................................................................................................. 3
Unit 6: Polynomial Graphs
Unit 6: Vocabulary ................................................................................................................................. S 1
Lesson 1: Modeling with Polynomials – The Cardboard Box Problem ................................................. S 11
Lesson 2: Modeling with Polynomials – Using Equations .................................................................... S 19
Lesson 3: Multiplying Polynomials ....................................................................................................... S 25
Lesson 4: Dividing Polynomials ............................................................................................................ S 35
Lesson 5: Comparing Methods—Long Division, Again? ....................................................................... S 43
Lesson 6: Putting It All Together ........................................................................................................... S 53
Lesson 7: Graphs of Polynomial Functions .......................................................................................... S 59
Lesson 8: The Special Role of Zero in Graphing ................................................................................... S 67
Lesson 9: Mastering Factoring .............................................................................................................. S 75
Lesson 10: Graphing Polynomials ......................................................................................................... S 79
Lesson 11: Graphing Polynomials – Digging Deeper ........................................................................... S 87
Lesson 12: Structure in Graphs of Polynomial Functions ..................................................................... S 97
Unit 7: Rational Functions and Their Operations
Unit 7: Vocabulary .............................................................................................................................. S 109
Lesson 13: The Juice Can Problem ......................................................................................................S 115
Lesson 14: Rationally Speaking ...........................................................................................................S 121
Lesson 15: Multiplying and Dividing Rational Expressions ................................................................. S 129
Lesson 16: Adding and Subtracting Rational Expressions .................................................................. S 137
Lesson 17: Solving Rational Equations ...............................................................................................S 149

1Each lesson is ONE day, and ONE day is considered a 45-minute period.

Module 2: Polynomial, Rational, and Radical Relationships
1

This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This work is licensed under a
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Hart Interactive – Algebra II Module Overview M 2

ALGEBRA II

Lesson 18: Word Problems Leading to Rational Equations ................................................................ S 159
Lesson 19: Dividing Polynomials – What if there is a Remainder? ..................................................... S 169
Lesson 20: Dividing Polynomials Synthetically ................................................................................... S 177
Lesson 21: Polynomials Revisited: The Remainder Theorem ............................................................ S 181
Lesson 22: Think Fast! A Focus on Roots ........................................................................................... S 191
Lesson 23: Solving Complicated Radical Equations ............................................................................ S 201

Module 2: Polynomial, Rational, and Radical Relationships
2

This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This work is licensed under a
This file derived from ALG II-M1-TE-1.3.0-07.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Hart Interactive – Algebra II Module Overview M 2

ALGEBRA II

Algebra II • Module 2
Polynomial, Rational, and Radical
Relationships

OVERVIEW
In this module, you will draw on your foundation of the analogies between polynomial arithmetic and base-
ten computation, focusing on properties of operations, particularly the distributive property (A-SSE.2,
A-APR.1). You’ll connect multiplication of polynomials with multiplication of multi-digit integers and division
of polynomials with long division of integers (A-APR.1, A-APR.6). You will identify zeros of polynomials,
including complex zeros of quadratic polynomials, and make connections between zeros of polynomials and
solutions of polynomial equations (A-APR.3). You will explore the role of factoring, as both an aid to the
algebra and to the graphing of polynomials (A-SSE.2, A-APR.2, A-APR.3, F-IF.7c). You’ll continue to build
upon the reasoning process of solving equations as you solve polynomial, rational, and radical equations, as
well as linear and non-linear systems of equations (A-REI.1, A-REI.2, A-REI.6, A-REI.7). The module
culminates with the fundamental theorem of algebra as the ultimate result in factoring. You’ll pursue
connections to applications in prime numbers in encryption theory, Pythagorean triples, and modeling
problems.
An additional theme of this module is that the arithmetic of rational expressions is governed by the same
rules as the arithmetic of rational numbers. You’ll use appropriate tools to analyze the key features of a
graph or table of a polynomial function and relate those features back to the two quantities that the function
is modeling in the problem (F-IF.7c).

Module 2: Polynomial, Rational, and Radical Relationships
3

This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This work is licensed under a
This file derived from ALG II-M1-TE-1.3.0-07.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Hart Interactive – Algebra II Module Overview M 1
ALGEBRA II

Module 2: Polynomial, Rational, and Radical Relationships
4

This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This work is licensed under a
This file derived from ALG II-M1-TE-1.3.0-07.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Hart Interactive – Algebra 2

Unit 6 Vocabulary

ALGEBRA II • MODULE 2

Knowledge Vocabulary
Lesson Definition Picture/Example/Notation
Rating* Terms
A function that contains 1 or more
Polynomial ____________or ____________terms.
1
Function The variables may be to any non-negative
power.
Mathematical modeling is the process of
using _________, ____________and
1 Modeling
___________to represent real world
situations.
Square Root
1 This function has the form___________.
Function
A ______-degree polynomial function of
Quadratic the form ax2 + bx + c = y and a, b, and c
1
Function
are real numbers. The graph is called a
____________ and has a U shape.
A ______-degree polynomial function of
the form ____________and b and m are
Linear
1 real numbers. The equation of a linear
Function
function has either one or two variables
raised only to the ______ power.

Knowledge Rating: N = I have no knowledge of the word.
S = I’ve seen the word, but I’m not sure what it means.
U = I understand this word and can use it correctly.

Module 2: Polynomial, Rational and Radical Relationships
Unit 6: Polynomial Graphs S.1

This work is licensed under a
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from GEO-M1-TE-1.3.0 -07.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Hart Interactive – Algebra 2 Unit 6 Vocabulary M 2
ALGEBRA II

Knowledge Vocabulary
Lesson Definition Picture/Example/Notation
Rating* Terms
A regression equation models the
____________between two or more
Regression
2 variables. It is a measure to which
Equations
researchers can ____________one
variable from another.
The domain is the set of values of the
independent variable for which a function
2 Domain is defined. This is usually the ______-
values, sometimes called the
“____________” values.
The range is the set of values of the
dependent variable for which a function
2 Range is defined. This is usually the ______-
values, sometimes called the
“____________” values.
The factored form of an expression is
Factored composed of the ____________of
2
Form factors, rather than a sum or difference
of terms.
A polynomial is a monomial or the
Terms of a ______or ____________of monomials.
2
Polynomial Each monomial is called a term of the
polynomial.
The highest degree of a polynomial’s
Degree of a terms. The degree of a term is the
2
Polynomial ______ of the exponents of the
variables that appear in it.

Knowledge Rating: N = I have no knowledge of the word.
S = I’ve seen the word, but I’m not sure what it means.
U = I understand this word and can use it correctly.

Module 2: Polynomial, Rational and Radical Relationships
Unit 6: Polynomial Graphs S.2

This work is licensed under a
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from GEO-M1-TE-1.3.0-07.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Hart Interactive – Algebra 2 Unit 6 Vocabulary M 2
ALGEBRA II

Knowledge Vocabulary
Lesson Definition Picture/Example/Notation
Rating* Terms
A ____________or
____________multiplied with a
2 Coefficient
variable or an unknown quantity in an
algebraic term.
Terms whose ____________and their
2 Like Terms ____________are the same. The
coefficients may be different.
Tabular An organizational tool used to
3
Method ____________polynomials
To ____________out the parts of an
3 Distribute expression. Distributing is the
opposite of ____________.
A number or quantity that when
3 Factor ____________with another produces
a given number or expression
Difference of
3 a2−b2 =______________
Squares

Knowledge Rating: N = I have no knowledge of the word.
S = I’ve seen the word, but I’m not sure what it means.
U = I understand this word and can use it correctly.

Module 2: Polynomial, Rational and Radical Relationships
Unit 6: Polynomial Graphs S.3

This work is licensed under a
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from GEO-M1-TE-1.3.0-07.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Hart Interactive – Algebra 2 Unit 6 Vocabulary M 2
ALGEBRA II

Knowledge Vocabulary
Lesson Definition Picture/Example/Notation
Rating* Terms

Difference of
3 a3−b3 =______________
Cubes

3 Sum of Cubes a3+b3 =______________
An algebraic expression with only
4 Monomial
______ term.
An algebraic expression of the sum or
4 Binomial
difference of ______ terms
An algebraic expression of the sum or
4 Trinomial
difference of ______ terms

A result obtained by ____________
4 Quotient
one quantity by another

A result obtained by ____________
4 Product
one quantity by another.

Reverse An organizational tool used to
4
Tabular Method ____________ polynomials.

Knowledge Rating: N = I have no knowledge of the word.
S = I’ve seen the word, but I’m not sure what it means.
U = I understand this word and can use it correctly.

Module 2: Polynomial, Rational and Radical Relationships
Unit 6: Polynomial Graphs S.4

This work is licensed under a
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from GEO-M1-TE-1.3.0-07.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.