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Algebra

Elementary to Advanced - Polynomials and Roots

4.9 Filled star Filled star Filled star Filled star Half star
Based on 135 ratings
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Joseph W. Cutrone, PhD

This course is the final course in a three part algebra sequence, In this course, students extend their knowledge of more advanced functions, and apply and model them using both algebraic and geometric techniques. This course enables students to make logical deductions and arrive at reasonable conclusions. Such skills are crucial in today's world. Knowing how to analyze quantitative information for the purpose of making decisions, judgments, and predictions is essential for understanding many important social and political issues. Quantitative Skills and Reasoning provides students the skills needed for evaluating such quantitatively-based arguments.

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This course is the final course in a three part algebra sequence, In this course, students extend their knowledge of more advanced functions, and apply and model them using both algebraic and geometric techniques. This course enables students to make logical deductions and arrive at reasonable conclusions. Such skills are crucial in today's world. Knowing how to analyze quantitative information for the purpose of making decisions, judgments, and predictions is essential for understanding many important social and political issues. Quantitative Skills and Reasoning provides students the skills needed for evaluating such quantitatively-based arguments.

This class is important as the mathematical ideas it treats and the mathematical language and symbolic manipulation it uses to express those ideas are essential for students who will progress to calculus, statistics, or data science.

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What's inside

Syllabus

Module 1: Exponentials
The ubiquitous occurrence of the exponential function in pure and applied mathematics has led mathematician W. Rudin to opine that the exponential function is "the most important function in mathematics". In applied settings, exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change (i.e., percentage increase or decrease) in the dependent variable. This occurs widely in the natural and social sciences, as in a self-reproducing population, a fund accruing compound interest, or a growing body of manufacturing expertise. Thus, the exponential function also appears in a variety of contexts within physics, chemistry, engineering, mathematical biology, and economics.
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Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Covers a variety of topics including exponentials, polynomials, roots, and applications, making it comprehensive for students needing to strengthen their algebra foundation
Helps students develop their logical reasoning and quantitative analysis skills, which are essential for success in higher-level math courses and various fields
Taught by Joseph W. Cutrone, PhD, who has extensive experience and expertise in mathematics education, ensuring the course is well-structured and rigorous
Part of a three-part algebra sequence, providing a solid foundation for students who plan to pursue calculus, statistics, or data science
Utilizes a variety of teaching methods, including videos, readings, and discussions, catering to diverse learning styles and keeping the course engaging
Requires students to have a strong foundation in algebra, making it more suitable for intermediate learners

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Reviews summary

Algebra: foundational for stem careers

According to learners, this course offers a solid foundation in advanced algebra, particularly beneficial for those preparing for calculus, statistics, or data science. Many highlight the instructor's clear explanations and engaging lectures as key strengths, making complex topics accessible. While the course title suggests a broad spectrum, some found the initial modules too elementary or the transition to advanced concepts somewhat abrupt, indicating a need for strong prerequisite knowledge. The problem sets are generally seen as helpful, though some desired more varied or challenging practice. Overall, students find it a valuable preparation for higher-level quantitative studies.
Practice problems are helpful but could benefit from more variety.
"The quizzes were good for reinforcing what I learned in the lectures for each module."
"I liked the practice problems, but sometimes wished for more challenging examples to solidify my understanding."
"The problem sets were generally helpful for understanding concepts, though some felt repetitive."
Excellent preparation for advanced quantitative studies.
"This course really solidified my algebra skills, making me feel ready for calculus."
"I needed this for statistics, and it delivered a strong foundation for those concepts."
"It's truly essential for anyone looking to pursue data science or more advanced mathematics."
The instructor effectively clarifies complex algebraic concepts.
"The instructor's explanations were incredibly clear, making even tough concepts easy to grasp."
"I appreciate how the instructor broke down the material, it really made a difference in my understanding."
"The lectures are engaging and well-structured, a true testament to the instructor's expertise."
Pacing shifts from foundational to rapid for advanced topics.
"The beginning felt a bit slow, covering elementary concepts I already knew from prior studies."
"The jump from elementary to advanced concepts in the later modules was quite steep and challenging."
"I found the transition challenging; more intermediate steps or examples would have been helpful to bridge the gap."
A solid pre-algebra/algebra 1 background is beneficial.
"Make sure you have a strong grasp of algebra basics before diving into this course."
"I struggled because I underestimated the prior knowledge needed for the advanced parts, especially with polynomials."
"This course assumes a certain level of familiarity with foundational algebra, so review if needed."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Algebra: Elementary to Advanced - Polynomials and Roots with these activities:
Algebra Review Notebook
Compiling all your notes, assignments, and practice problems into a comprehensive notebook will serve as a valuable reference and study tool throughout the course.
Show steps
  • Gather all your class notes, homework assignments, and practice problems.
  • Organize the materials by topic or lesson.
  • Summarize key concepts and formulas in your own words.
  • Include additional notes or examples to enhance your understanding.
Linear Equation Refresher
Reviewing the basics of linear equations will strengthen your foundation and prepare you for more advanced topics in algebra.
Browse courses on Linear Equations
Show steps
  • Review the steps for solving linear equations in one variable.
  • Practice solving equations with different coefficients and variables.
  • Identify the slope and y-intercept of linear equations from their equations.
Review Pre-Algebra and Algebra
By refreshing your knowledge of Pre-Algebra and Algebra, you will be reviewing the fundamentals that this course builds upon.
Show steps
  • Review the order of operations and properties of real numbers.
  • Practice solving one-step equations.
  • Review solving multi-step equations.
Eight other activities
Expand to see all activities and additional details
Show all 11 activities
Review: Precalculus by Stewart, 7th Edition
Reading and reviewing a standard precalculus textbook will provide a comprehensive foundation for the topics covered in this algebra course.
View Notetaking Guide for Stewart's Calculus: Early... on Amazon
Show steps
  • Read the assigned chapters and take notes on key concepts.
  • Solve practice problems at the end of each chapter to reinforce your understanding.
  • Summarize the main ideas and formulas in your own words.
Applications of Quadratics Review
Practicing a variety of quadratic application problems will strengthen your ability to apply algebraic concepts to real-world scenarios.
Browse courses on Quadratic Functions
Show steps
  • Solve word problems involving maximum or minimum values.
  • Use quadratic equations to model and solve projectile motion problems.
  • Apply the quadratic formula to find the roots of quadratic equations in context.
Polynomial Graphing Activity
Creating a program to graph polynomials will reinforce your understanding of their behavior, including things like degree, roots, and asymptotes.
Browse courses on Functions
Show steps
  • Start by choosing a programming language and researching libraries for graphing.
  • Design a function to take in polynomial coefficients and number of points to evaluate.
  • Create a loop to evaluate the polynomial at each point and store the result.
  • Use a library or built-in function to plot the points and connect them with a line.
Exponential Function Practice
Solving a variety of exponential equations and problems will help you develop a strong foundation in the topic and improve your problem-solving skills.
Browse courses on Exponents
Show steps
  • Find the value of exponential expressions with different bases and exponents.
  • Solve exponential equations by rewriting them in logarithmic form.
  • Graph exponential functions and identify their key features, such as intercepts and asymptotes.
Khan Academy: Solving Exponential Equations
This tutorial provides a step-by-step guide on how to solve exponential equations, which are covered in Module 1 of this course.
Show steps
  • Watch the video tutorial on solving exponential equations.
  • Complete the practice exercises provided.
Roots of Unity Tutorial
Following an in-depth tutorial on roots of unity will expand your understanding of complex numbers and their applications in various fields, such as electrical engineering.
Browse courses on Complex Numbers
Show steps
  • Review the basics of complex numbers and polar form.
  • Learn the definition and properties of roots of unity.
  • Solve problems involving roots of unity, such as finding their sum or product.
Polynomial Long Division Practice
Polynomials are covered in Module 2 of this course, and polynomial long division is a key skill for working with polynomials. This drill will give you the practice you need to master this skill.
Browse courses on Polynomials
Show steps
  • Solve 10 polynomial long division problems.
  • Check your answers using a calculator or online tool.
Algebra Tutoring
Tutoring other students in algebra will strengthen your own understanding of the subject and develop your communication and teaching skills.
Show steps
  • Offer your services as a tutor to classmates or students in lower-level algebra courses.
  • Prepare lesson plans and materials to help students understand specific concepts.
  • Meet with students regularly to provide support and guidance.
  • Reflect on your tutoring experiences and identify areas for improvement.

Career center

Learners who complete Algebra: Elementary to Advanced - Polynomials and Roots will develop knowledge and skills that may be useful to these careers:
Actuary
Actuaries use mathematics and statistics to assess risk and uncertainty. They work in a variety of industries such as insurance, finance, and consulting. Algebra: Elementary to Advanced - Polynomials and Roots would be particularly useful for actuaries who work with insurance companies. The course provides a strong foundation in the mathematics used to calculate insurance premiums and to develop risk management strategies.
See salaries and explore the career path for Actuary
Data Scientist
Data scientists use mathematics and statistics to extract knowledge from data. They work in a variety of industries such as technology, finance, and healthcare. Algebra: Elementary to Advanced - Polynomials and Roots would be particularly useful for data scientists who work with large datasets. The course provides a strong foundation in the mathematics used to analyze data and to develop predictive models.
See salaries and explore the career path for Data Scientist
Financial Analyst
Financial analysts use mathematics and statistics to analyze financial data and make investment recommendations. They work in a variety of industries such as investment banking, asset management, and hedge funds. Algebra: Elementary to Advanced - Polynomials and Roots would be particularly useful for financial analysts who work with complex financial models. The course provides a strong foundation in the mathematics used to analyze financial data and to develop investment strategies.
See salaries and explore the career path for Financial Analyst
Operations Research Analyst
Operations research analysts use mathematics and statistics to solve business problems. They work in a variety of industries such as manufacturing, logistics, and healthcare. Algebra: Elementary to Advanced - Polynomials and Roots would be particularly useful for operations research analysts who work with complex mathematical models. The course provides a strong foundation in the mathematics used to analyze business problems and to develop solutions.
See salaries and explore the career path for Operations Research Analyst
Quantitative Analyst
Quantitative analysts use mathematics and statistics to analyze financial data and make investment decisions. They work in a variety of industries such as investment banking, asset management, and hedge funds. Algebra: Elementary to Advanced - Polynomials and Roots would be particularly useful for quantitative analysts who work with complex financial models. The course provides a strong foundation in the mathematics used to analyze financial data and to develop investment strategies.
See salaries and explore the career path for Quantitative Analyst
Statistician
Statisticians use mathematics and statistics to collect, analyze, and interpret data. They work in a variety of industries such as healthcare, education, and government. Algebra: Elementary to Advanced - Polynomials and Roots would be particularly useful for statisticians who work with complex statistical models. The course provides a strong foundation in the mathematics used to analyze data and to develop statistical models.
See salaries and explore the career path for Statistician
Economist
Economists use mathematics and statistics to analyze economic data and to develop economic policies. They work in a variety of industries such as government, academia, and consulting. Algebra: Elementary to Advanced - Polynomials and Roots may be useful for economists who work with complex economic models. The course provides a foundation in the mathematics used to analyze economic data and to develop economic models.
See salaries and explore the career path for Economist
Computer Programmer
Computer programmers use mathematics and logic to design and develop computer programs. They work in a variety of industries such as technology, finance, and healthcare. Algebra: Elementary to Advanced - Polynomials and Roots may be useful for computer programmers who work with complex algorithms. The course provides a foundation in the mathematics used to design and develop computer programs.
See salaries and explore the career path for Computer Programmer
Software Engineer
Software engineers use mathematics and logic to design and develop software systems. They work in a variety of industries such as technology, finance, and healthcare. Algebra: Elementary to Advanced - Polynomials and Roots may be useful for software engineers who work with complex software systems. The course provides a foundation in the mathematics used to design and develop software systems.
See salaries and explore the career path for Software Engineer
Mechanical Engineer
Mechanical engineers use mathematics and physics to design and develop mechanical systems. They work in a variety of industries such as manufacturing, automotive, and aerospace. Algebra: Elementary to Advanced - Polynomials and Roots may be useful for mechanical engineers who work with complex mechanical systems. The course provides a foundation in the mathematics used to design and develop mechanical systems.
See salaries and explore the career path for Mechanical Engineer
Electrical Engineer
Electrical engineers use mathematics and physics to design and develop electrical systems. They work in a variety of industries such as power, telecommunications, and electronics. Algebra: Elementary to Advanced - Polynomials and Roots may be useful for electrical engineers who work with complex electrical systems. The course provides a foundation in the mathematics used to design and develop electrical systems.
See salaries and explore the career path for Electrical Engineer
Civil Engineer
Civil engineers use mathematics and physics to design and develop civil infrastructure. They work in a variety of industries such as construction, transportation, and water resources. Algebra: Elementary to Advanced - Polynomials and Roots may be useful for civil engineers who work with complex civil infrastructure projects. The course provides a foundation in the mathematics used to design and develop civil infrastructure projects.
See salaries and explore the career path for Civil Engineer
Chemical Engineer
Chemical engineers use mathematics and chemistry to design and develop chemical processes. They work in a variety of industries such as chemicals, pharmaceuticals, and energy. Algebra: Elementary to Advanced - Polynomials and Roots may be useful for chemical engineers who work with complex chemical processes. The course provides a foundation in the mathematics used to design and develop chemical processes.
See salaries and explore the career path for Chemical Engineer
Biomedical Engineer
Biomedical engineers use mathematics and biology to design and develop biomedical devices and systems. They work in a variety of industries such as healthcare, pharmaceuticals, and biotechnology. Algebra: Elementary to Advanced - Polynomials and Roots may be useful for biomedical engineers who work with complex biomedical devices and systems. The course provides a foundation in the mathematics used to design and develop biomedical devices and systems.
See salaries and explore the career path for Biomedical Engineer
Environmental Engineer
Environmental engineers use mathematics and science to design and develop solutions to environmental problems. They work in a variety of industries such as government, consulting, and manufacturing. Algebra: Elementary to Advanced - Polynomials and Roots may be useful for environmental engineers who work with complex environmental problems. The course provides a foundation in the mathematics used to design and develop solutions to environmental problems.
See salaries and explore the career path for Environmental Engineer

Reading list

We've selected eight books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Algebra: Elementary to Advanced - Polynomials and Roots.
Cover image
Neural Networks are Homeomorphisms
Save
Classic text on Algebra which may be useful as a reference tool for students who are interested in learning more about the subject.
Neural Networks are Homeomorphisms: An Introduction...
Paperback
$$
Cover image
Lie Algebras
Save
Classic text on Algebra which may be useful as a reference tool for students who are interested in learning more about the subject.
Lie Algebras (Dover Books on Mathematics)
Kindle Edition
$
Cover image
Residues and Duality
Save
May be useful as a supplemental resource for students who are interested in learning more about Algebraic Geometry.
Residues and Duality
Paperback
Check
Residues and Duality
Kindle Edition
Check
Cover image
ELEMENTS OF ALGEBRAIC TOPOLOGY
Save
May be useful as a supplemental resource for students who are interested in learning more about Topology.
Elements Of Algebraic Topology
Kindle Edition
$$$
Cover image
More Explorations in Complex Functions
Save
May be useful as a supplemental resource for students who are interested in learning more about Analysis.
More Explorations in Complex Functions (Graduate...
Paperback
$$$
Cover image
Discrete Mathematics and Its Applications
Save
May be useful as a supplemental resource for students who are interested in learning more about Discrete Mathematics.
Discrete Mathematics and Its Applications
Paperback
$$$
Discrete Mathematics and Its Applications
Hardcover
$$$$
Student's Solutions Guide for Discrete Mathematics...
Paperback
$$$$
Connect Access Card for Discrete Mathematics and...
Printed Access Code
$$
Cover image
Mathematical Proofs
Save
May be useful as a supplemental resource for students who are interested in learning more about Mathematical Proofs.
Mathematical Proofs: A Transition to Advanced...
Hardcover
$$$$
Mathematical Proofs: A Transition to Advanced...
Hardcover
$$$$
Mathematical Proofs: A Transition to Advanced...
Hardcover
$$$$
Mathematical Proofs: A Transition to Advanced...
Kindle Edition
$$$
A First Course in Abstract Algebra (Seventh Edition)
Save
May be useful as a supplemental resource for students who are interested in learning more about abstract Algebra.
A First Course in Abstract Algebra (Seventh Edition)
Paperback
Check
A First Course in Abstract Algebra (Seventh Edition)
Kindle Edition
Check

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Course image
Rating
4.9 Filled star Filled star Filled star Filled star Half star
Effort
9 hours to complete
Level
Introductory
Via
Coursera
Institution
Johns Hopkins University
Instructor
Joseph W. Cutrone, PhD
Language
English
Transcripts
Español Français Português Deutsch Italiano 中文 العربية 한국어 日本語 हिंदी Nederlands Svenska Pусский Türkçe Polski Ελληνικά українська мова Bahasa Indonesia ไทย қазақша
This course belongs to a collection called Algebra: Elementary to Advanced. It's comprised of three courses:
  1. Algebra: Elementary to Advanced - Polynomials and Roots (viewing)
  2. Algebra: Elementary to Advanced - Functions & Applications
  3. Algebra: Elementary to Advanced - Equations & Inequalities
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Covers a variety of topics including exponentials, polynomials, roots, and applications, making it comprehensive for students needing to strengthen their algebra foundation
Helps students develop their logical reasoning and quantitative analysis skills, which are essential for success in higher-level math courses and various fields
Taught by Joseph W. Cutrone, PhD, who has extensive experience and expertise in mathematics education, ensuring the course is well-structured and rigorous
Part of a three-part algebra sequence, providing a solid foundation for students who plan to pursue calculus, statistics, or data science
Utilizes a variety of teaching methods, including videos, readings, and discussions, catering to diverse learning styles and keeping the course engaging
Requires students to have a strong foundation in algebra, making it more suitable for intermediate learners
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