MTH 65: Algebra 2
- Page ID
- 182298
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This book is your guide to building a strong and connected foundation in algebra. We’ll begin by sharpening essential tools—order of operations, fractions, and linear equations—that set the stage for every topic that follows. From there, you’ll deepen your understanding of algebraic structure by working with polynomials, exponents, and patterns that reveal how math models the world around us. As you progress, you’ll unlock the power of roots and radicals, learning how to reverse powers, simplify complex expressions, and solve new types of equations. Finally, we’ll explore absolute value, connecting algebra to real-world ideas of distance, tolerance, and precision. Together, these skills form a toolkit that will help you solve problems with confidence, think critically, and prepare for the advanced math and applications that lie ahead.
- Preface
- In this preface, you’ll find a welcome message to set the stage for your learning, guidance on how to use the book effectively, acknowledgments of those who contributed to its creation, and a table of contents to help you navigate the material. This section will help you get oriented and ready to make the most of the resources ahead.
- Unit 0: Prerequesite Review
- Before we dive into new algebra skills, we’ll warm up with the most essential tools from previous math courses. In this unit, we’ll review order of operations, working with fractions, and solving linear equations and inequalities—everything from one-step equations to systems.
- Unit 1: Working With Polynomials
- In this unit, we build a strong foundation in polynomial expressions and exponents. We’ll learn how to add, subtract, multiply, and divide polynomials, and apply exponent rules to simplify expressions. We’ll explore special patterns, such as perfect square trinomials and the difference of squares. As we practice simplifying and factoring, we’ll see how algebra helps us model patterns and quantities in compact, powerful ways, preparing us for more advanced algebra and applications.
- Unit 2: Roots and Radicals
- Now it’s time to explore roots and radicals—expressions that help us reverse powers. We’ll start with square roots and then go deeper into simplifying, estimating, and operating with radicals. You’ll learn how to add, subtract, multiply, and divide radical expressions, solve square root equations, and convert between radicals and rational exponents. These skills are essential in science, geometry, and real-world modeling, providing new ways to express and simplify complex relationships.
- Unit 3: Measuring Magnitude
- In this final unit, we’ll explore absolute value as a way to measure distance—how far a number is from zero, no matter the direction. We’ll learn how to solve equations and inequalities involving absolute value, both symbolically and graphically. With the help of tools like Desmos, we’ll see how absolute value defines ranges, tolerances, and real-world limits. Whether it’s GPS coordinates or error margins in science, absolute value helps us define what "close enough" means.
- Unit 4: Practice Problem Answers
- This unit provides the answers to all the practice problems from the textbook. It’s here to help you confirm whether your solutions are correct and to support your learning by giving you immediate feedback. However, remember that knowing the final answer is only part of doing math. You’re still responsible for showing clear, step-by-step work that demonstrates your thinking and understanding.