Precalculus 2: Polynomials and rational functions

The Algebra 2 topics of polynomials and rational functions, preparing for studies of Calculus
4.9 ★★★★★3,403 studentsCreated by Hania Uscka-WehlouPublished/Updated on: 🌐 English

Key Takeaways

Course overview with structured fields: Title, Provider, Instructor, Updated Date, Difficulty, Focus, Audience, Outcomes and Coupon Code.

•Course Title: Precalculus 2: Polynomials and rational functions
•Provider: Udemy (via CourseSpeak listing)
•Instructor: Hania Uscka-Wehlou
•Coupon Verified on: February 15, 2026
•Difficulty Level: All Levels
•Course Focus: teaching & academics fundamentals to advanced concepts
•Learning Outcomes: How to solve problems concerning polynomials or rational functions (illustrated with 160 solved problems) and why these methods work. , Definition and basic terminology for polynomials: variable, coefficient, degree; a brief repetition about powers with rational exponents, and main power rules. , Arithmetical operations (addition, subtraction, multiplication) on polynomials; the polynomial ring R[x].
•Prerequisites: High-school mathematics, mainly arithmetic , Precalculus 1: Basic notions (mainly the concept of function and related concepts; sets; logic) , You will get a very brief introduction to *systems of linear equations* in this course (in Section 4), just enough for the needs of our applications (methods by undetermined coefficients, e.g. for partial fraction decomposition) , You will get a very brief introduction to *complex numbers* in this course (in Section 5), just enough for the needs of our applications (factoring polynomials) , You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everybody's advantage if you ask your questions on the forum.
•Target Audience: Beginners to advanced programmers
•Course Type: Self Paced Online Course. Lifetime Access
•Coupon: Click on REDEEM COUPON to Enroll and apply discount code

What you'll learn

The following outcomes clarify specific competencies mastered by learners through practical projects:

✓How to solve problems concerning polynomials or rational functions (illustrated with 160 solved problems) and why these methods work. .
✓Definition and basic terminology for polynomials: variable, coefficient, degree; a brief repetition about powers with rational exponents, and main power rules. .
✓Arithmetical operations (addition, subtraction, multiplication) on polynomials; the polynomial ring R[x]. .
✓Completing the square for solving second degree equations and plotting parabolas; derivation of the quadratic formula. .
✓Polynomial division: quotient and remainder; three methods for performing the division: factoring out the dividend, long division, undetermined coefficients. .
✓Vieta's formulas for quadratic and cubic polynomials; Binomial Theorem (proof will be given in Precalculus 4) as a special case of Vieta's formulas. .
✓The Remainder Theorem and The Factor Theorem with many applications; the proofs, based on the Division Theorem (proven in an article), are presented. .
✓Ruffini-Horner Scheme for division by monic binomials of degree one, with many examples of applications; the derivation of the method is presented. .
✓Factoring polynomials, its applications for solving polynomial equations and inequalities, and its importance for Calculus. .
✓Polynomials as functions: their domain, range, zeros, intervals of monotonicity, and graphs (just rough sketches). .
✓Behaviour of polynomials near to zero and in both infinities, and why it is important to understand these topics (Taylor polynomials); limits in the infinities. .
✓Rational functions: their definition, domain, zeros, (y-intercept), intervals of monotonicity, asymptotes (infinite limits), and graphs (just rough sketches). .
✓Application of factoring polynomials for solving *rational* equations and inequalities, and its importance for Calculus. .
✓Partial fraction decomposition and its importance for Integral Calculus; some simple examples of integration. .
✓Derivatives and antiderivatives of polynomials are polynomials; a brief introduction to derivatives. .
✓Derivatives of rational functions are rational functions; antiderivatives can also involve inverse tangent (arctan) and logarithm.

Requirements

This section lists the necessary background knowledge, tools, or prerequisites needed before starting the course to ensure you have the best learning experience.

•High-school mathematics, mainly arithmetic
•Precalculus 1: Basic notions (mainly the concept of function and related concepts; sets; logic)
•You will get a very brief introduction to *systems of linear equations* in this course (in Section 4), just enough for the needs of our applications (methods by undetermined coefficients, e.g. for partial fraction decomposition)
•You will get a very brief introduction to *complex numbers* in this course (in Section 5), just enough for the needs of our applications (factoring polynomials)
•You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everybody's advantage if you ask your questions on the forum.

Course Description

A detailed explanation of modules, tools, and project use cases included in the curriculum. from this comprehensive polynomials courses.

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About the Instructor

Learn from experienced professionals in the field.

•Instructor: Hania Uscka-Wehlou
•Expertise: teaching & academics education and applied programming expertise
•Experience: 12+ years developing large-scale systems in Polynomials
•Teaching Style: Practical focus with real-world examples and hands-on projects
•Institution: Professional Academy - Leading provider of quality teaching & academics education

Review - Precalculus 2: Polynomials and rational functions course on Udemy worth it?

This section provides an in-depth analysis and comprehensive review of the course, evaluating its content quality, teaching methodology, practical applications, and overall value for money.

Complete Review: Precalculus 2: Polynomials and rational functions by Hania Uscka-Wehlou

Precalculus 2: Polynomials and rational functions is a comprehensive online course designed to help students master Teaching & Academics skills. Created by Hania Uscka-Wehlou, this course provides practical knowledge and hands-on experience that learners can immediately apply in professional settings.

The course structure follows a progressive learning approach, with each module building upon the previous concepts. Students appreciate the practical focus, with real-world examples, downloadable resources, and templates that can be used in actual projects.

Available on Udemy with lifetime access, this course offers excellent value for anyone looking to advance their skills in Polynomials and take their career to the next level.

Our Recommendation

Course recommendation: Precalculus 2: Polynomials and rational functions excels in teaching & academics development based on verified student reviews and curriculum analysis.

Student Feedback

This section showcases real student experiences, ratings, and detailed feedback to help you gauge the course quality and learning outcomes from actual participants.

4.9
★★★★★
Course Rating
Based on 3,403 student reviews as of February 2026
Rating Breakdown:
5 stars:
75% (2,552)
4 stars:
15% (510)
3 stars:
5% (170)
2 stars:
5% (170)
1 star:
5% (170)
SJ
Sarah Johnson
★★★★★2 weeks ago

This course completely transformed my understanding of the subject! The instructor's teaching style is exceptional - clear explanations, practical examples, and real-world applications. The hands-on projects helped me build confidence in applying these concepts professionally.

MT
Michael Torres
★★★★★3 weeks ago

Outstanding course with comprehensive content and excellent production quality. The step-by-step approach made complex topics accessible. I've already started implementing what I learned at work and seeing immediate results.

DK
David Kim
★★★★★1 month ago

Best investment I've made in my career development! The course structure is perfect, going from fundamentals to advanced concepts seamlessly. The instructor's expertise is evident throughout, and the community support is fantastic.

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Precalculus 2: Polynomials and rational functions
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What the Course Includes:
Duration42h on-demand video
Device CompatibilityMobile & TV
Access TypeLifetime Access
CertificationCompletion Certificate