Mathematics & statistics
Basic Algebra with Applications
Ivan G. Zaigralin
Samizdat · 6th edition; copyright 2017–2023 · English · Published 2023
Algebra from mathematical expressions and real-number axioms through equations, functions and applications, with worked exercises and answers.
- Learning stage
- High school
- Prerequisites
- Arithmetic and readiness to learn elementary algebra.
- PDF pages
- 513 in this file
- Editorial review
- 2026-10-29
Contents
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Contents
Chapter 1. Concepts
Chapter 1. Concepts
1. Expressions, Relations, and Substitution
2. Real Number Axioms
3. The Number Line and Sets of Numbers
4. Properties of Real Numbers
5. Order of Operations
6. Prime Numbers
7. Fractions and Rationals
8. Fraction Addition
9. Translation
Practice Test 1
Chapter 2. Linear Equations
Chapter 2. Linear Equations
1. Properties of Equations
2. Solving Linear Equations
3. Linear Formulas
4. Percent
5. Applications
6. Linear Inequalities
Practice Test 2
Chapter 3. Graphing
Chapter 3. Graphing
1. Reading and Constructing Graphs
2. Graphing Linear Equations
3. Intercepts
4. Slope
5. Slope-Intercept Form
6. Point-Slope Form
7. Function Notation
Practice Test 3
Chapter 4. Linear Systems
Chapter 4. Linear Systems
1. Graphing Systems of Equations
2. Substitution
3. Elimination
4. Applications of Systems
5. Multivariate Linear Inequalities
Practice Test 4
Chapter 5. Polynomial Expressions
Chapter 5. Polynomial Expressions
1. Integer Exponent
2. Properties of Exponent
3. Introduction to Polynomials
4. Sums of Polynomials
5. Products of Polynomials
6. Special Products
7. Quotients of Polynomials
8. Negative Exponent
Practice Test 5
Chapter 6. Factoring Polynomials
Chapter 6. Factoring Polynomials
1. Greatest Common Factor
2. Grouping
3. Factoring x2 + bx + c
4. Factoring ax2 + bx + c
5. Factoring Special Products
6. General Factoring Strategy
7. Solving Equations by Factoring
8. Factoring Applications
Practice Test 6
Chapter 7. Rational Expressions
Chapter 7. Rational Expressions
1. Simplifying Rational Expressions
2. Products of Rational Expressions
3. LCD for Rational Expressions
4. Sums of Rational Expressions
5. Complex Fractions
6. Equations with Rational Expressions
Practice Test 7
Chapter 8. Radicals
Chapter 8. Radicals
1. Introduction to Radicals
2. Products with Square Roots
3. Quotients with Square Roots
4. Sums with Square Roots
5. Equations with Square Roots
6. Applications to Right Triangles
7. Rational Exponent
Practice Test 8
Chapter 9. Quadratic Equations
Chapter 9. Quadratic Equations
1. Complex Numbers
2. Square Root Property
3. Completing the Square
4. Quadratic Formula
Practice Final
Appendix A. To Instructors
Appendix A. To Instructors
1. Lecture Notes
Appendix B. To Developers
Appendix B. To Developers
1. Contributing
2. Document Formatting Guidelines
3. To Do
4. Working with the Source
5. Acknowledgments
Index
Sources and permissions
The author and publisher remain the source of this textbook. Permission information applies to the specific files in this edition.
Author, publisher, and discovery sources
Authors: Ivan G. Zaigralin
Publisher: Samizdat
- Discovered through Open Textbook Library: Source record · Checked 2026-10-29
- Discovered through Open Textbook Library: Source record · Checked 2026-10-25
CC BY-SA 4.0
Basic Algebra with Applications, sixth edition, Ivan G. Zaigralin, copyright 2017–2023, Samizdat, CC BY-SA 4.0. Cover design copyright 2018 Derrick Santiago. Original PDF unchanged; all original credits retained; no endorsement implied.
Changes: Original PDF bytes are unchanged. Catalog metadata and page viewing are supplied by iReadAll. No endorsement implied. Structured extraction, audio, translation and independent image redistribution are not approved.
Checked 2026-10-29