Precalculus 2: Polynomials and rational functions
The Algebra 2 topics of polynomials and rational functions, preparing for studies of Calculus
What you'll learn in this Udemy Course
- ✓ 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.
Udemy Coupon Requirements
- 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.
About This Udemy Coupon
⚡ Limited Time Offer
Coupon valid until end of April 2026
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What is Precalculus 2: Polynomials and rational functions?
Precalculus 2: Polynomials and rational functions is a 42h online course on Udemy taught by Hania Uscka-Wehlou. It covers Polynomials and is designed for learners who want to how to solve problems concerning polynomials or rational functions (illustrated with 160 solved problems) and why these methods work. . With 3,452 students enrolled and a 4.9 star rating, it is one of the top-rated courses in Polynomials on Udemy. Use the coupon above to access it at 94% OFF ($9.99).
About the Instructor
Hania Uscka-Wehlou
Udemy Instructor · Teaching & Academics Expert
Hania Uscka-Wehlou is an expert instructor on Udemy specializing in Teaching & Academics. Their course "Precalculus 2: Polynomials and rational functions" has helped 3,452 students master Polynomials with a 4.9 star rating.
Course Information
Platform
Udemy
Instructor
Hania Uscka-Wehlou
Duration
42h
Language
English
Category
Teaching & Academics · Polynomials
Rating
Price
Last Updated
March 2026
Related Topics
Andrew Derek
Expert ReviewerAndrew Derek is a lead editor and course analyst at CoursesWyn with over 8 years of experience in online education and digital marketing. He meticulously audits every Udemy coupon and course syllabus to ensure students get the highest quality learning materials at the best possible price.
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Frequently Asked Questions
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How long is Precalculus 2: Polynomials and rational functions?
Precalculus 2: Polynomials and rational functions is approximately 42h long. Udemy gives you lifetime access so you can learn at your own pace and revisit content anytime.
What will I learn in Precalculus 2: Polynomials and rational functions?
In Precalculus 2: Polynomials and rational functions by Hania Uscka-Wehlou, you will learn: 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]. . The course covers Polynomials with 42h of hands-on content.
What is Precalculus 2: Polynomials and rational functions?
Precalculus 2: Polynomials and rational functions is a 42h online course on Udemy taught by Hania Uscka-Wehlou. It covers Teaching & Academics with a 4.9 star rating from 3,452 enrolled students. Use our verified coupon to access it at $9.99 (94% OFF).