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Johns Hopkins University via Coursera
Honors Algebra 2: Polynomials and Complex Numbers
Overview
Honors Algebra 2: Polynomials and Complex Numbers
By the end of this course, learners will be able to analyze, graph, and transform polynomial functions, apply techniques such as factoring, division, and the Remainder and Factor Theorems to solve higher-order equations, and use the Fundamental Theorem of Algebra to understand the complete set of polynomial solutions. They will also develop fluency with complex numbers, performing arithmetic operations, representing them in both algebraic and geometric forms, and applying them to solve equations that have no real solutions.
As the second course in the three-part Honors Algebra 2 specialization, this class moves beyond routine algebraic skills to build deep mathematical reasoning. Students will see how polynomials and complex numbers provide the foundation for modern algebra, engineering, and physics, while practicing advanced problem-solving strategies that encourage both precision and creativity.
What makes this course unique is its balance of rigor and accessibility. Learners progress through challenging concepts with step-by-step guidance, visual explanations, and real-world applications that demonstrate why these topics matter. Completing this course prepares students not only to excel in advanced high school mathematics but also to transition confidently into college-level coursework.
Syllabus 3
- Quadratic Polynomials and Complex Roots 3 hours
You’ve already worked with quadratic equations and discovered how powerful they are for modeling and problem-solving. But what happens when a quadratic has no real solutions? Does the journey stop there? Not at all—this is where mathematics becomes even more fascinating. In this module, you’ll be i…
- Polynomial Functions and Graphs 5 hours
Up to now, you’ve worked with linear and quadratic functions—two powerful tools for modeling relationships and solving problems. But these are just the beginning of a much bigger family of functions called polynomials. In this module, you’ll dive into polynomial functions of higher degree, uncoveri…
- Analyzing Polynomials 4 hours
As we complete our study of polynomials, it’s time to take a closer look at their most important features—their roots, or zeros. In this module, you’ll learn powerful techniques for finding and analyzing these solutions, building on your understanding of complex numbers to tackle equations that go…
Advantages and disadvantages
Advantages
- Structured courses with graded quizzes, assignments and deadlines you can reset.
- A shareable certificate from the university or company when you pay.
- Financial aid is often approved for students in India (apply 15 days before you need it).
- Taught by Johns Hopkins University, one of the strongest names in its field.
- Self-paced: start any time.
- A clear syllabus (3 parts) you can see before you start.
Disadvantages
- Paid after a 7-day free trial (Coursera Plus or per course).
- Some courses can be audited for free, but graded work and certificates need payment.
Some points apply to every course of this kind; see how we rank.
This course is paid. Here is how to take it for free
- Free trials: You can start a 7-day free trial for many individual courses, Specializations, or a Coursera Plus subscription to test full course features. Cancel before the seventh day if you do not want to be charged.
- Financial aid: If you cannot afford the fee for a certificate, you can apply for financial aid through the link on the course home page by filling out an application about your background and goals.
Taught by
- Joseph W. Cutrone, PhDAssociate Teaching Professor and Director of Online Programs, Mathematics
Johns Hopkins University is in Tier 1: world-leading universities and India's top institutes of our institution ranking (93/100).
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