Precalculus 2: Polynomials and rational functions, the name of the course is Precalculus 2: Polynomials and rational functions in mathematics, which was published by Yodami Academy. The topics that you will get to know at the end of this course:
1. Course introduction
2. General presentation with big picture and few spoilers
3. Exponents, expressions and polynomials
4. Linear equations and systems of equations
5. Quadratic polynomials
6. Factoring polynomials such as finding zeros of multiples is polynomials
7. Factoring polynomials: school versus reality
8. Polynomial equations and inequalities
9. Some topics from differential and integral calculus
10. Drawing (drawing) polynomials
11. More advanced topics in The case of polynomials
12. Rational functions and their domains
13. Rational equations and inequalities
15. Drawing (design) of rational functions
16. Partial fraction analysis
17. More advanced topics about rational functions
18. A few words on The case of power functions and algebraic functions
19. Additional items
Who is this course suitable for?
- Students who intend to study algebra, differential and integral calculus or real analysis
- High school students are curious about college math
- Anyone who wants to improve their high school math and gain a deeper understanding of the subject
- College and university students studying advanced courses who want to understand all the details (about polynomials or rational functions) that they may have missed in their previous studies.
- Students who want to learn about polynomials, for example for their college algebra class.
What you will learn in Precalculus 2: Polynomials and rational functions course:
- How to solve problems involving polynomials or exponential functions (illustrated by 160 solved problems) and why these methods work.
- Definition and basic terms for polynomials: variable, coefficient, degree. A brief recap on powers with rational powers and basic power rules.
- Arithmetic operations (addition, subtraction, multiplication) on polynomials.
- Polynomial loop R[x].
- Completing the square to solve quadratic equations and draw parabola.
- Derivation of quadratic formula of polynomial division: quotient and remainder.
- Three methods to do the division: factoring the dividend, long division, uncertain coefficients.
- Vieta formulas for quadratic and cubic polynomials.
- The 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 of the proof, based on the division theorem (proved in a paper), are presented.
- The Ruffini-Horner scheme for divisibility of first-order Mooney terms, with many examples of applications.
Instructor: Hania Uscka-Wehlou , Martin Wehlou
Education level: introductory to advanced
Number of lessons: 212
Duration of education: 42 hours 3 minutes
Precalculus 2 course headings: Polynomials and rational functions:
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, eg 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)
Polynomials and rational function Course pictures:
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Download part 1 – 5 GB
Download part 2 – 5 GB
Download part 3 – 5 GB
Download part 4-5 GB
Download part 5 – 5 GB
Download part 6 – 5 GB
Download part 7 – 4.27 GB
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