Insights By Scott Ernst

Project Autodidact

Project Details: https://insightsbyse.com/projectautodidact/

Scott Ernst Bio: https://insightsbyse.com/aboutscotternst/

Project Contact: InsightsBySE@protonmail.com

Progress Report Scope (S01-M02-D03-AllParts)

Stage 1 of 4: Review of Mathematics, Probability, and Statistics

Module 2 of 3: Statistics, Probability, and Advanced Algebra

Day 3 of 5: Advanced Algebra and Polynomials

Parts 1 through 9: See below (NOTE: Only 9 parts for these topics)

Summary Of Goals Achieved

1. Reviewed definition, concepts, notation, terminology, components, and properties of a polynomial expression
2. Reviewed procedures for performing operations on a polynomial expression (addition, subtraction, and multiplication).  NOTE: Division will be subsequently studied.
3. Reviewed similarities and differences in the applicability of simplifying a polynomial expression by common factoring methods (greatest common factor (GCF), grouping, trinomial factoring, special case – difference of squares, special case – perfect square trinomial, and special case – sum/difference of cubes)
4. Reviewed procedures for simplifying a polynomial expression by the factoring method of greatest common factor (GCF)
5. Reviewed procedures for simplifying a polynomial expression by the factoring method of grouping
6. Reviewed procedures for simplifying a polynomial expression by the factoring method of trinomial factoring
7. Reviewed procedures for simplifying a polynomial expression by the special case factoring method of difference of squares
8. Reviewed procedures for simplifying a polynomial expression by the special case factoring method of perfect square trinomial
9. Reviewed procedures for simplifying a polynomial expression by the special case factoring method of sum/difference of cubes
10. Reviewed similarities and differences in the applicability of solving a polynomial equation by the factoring method, the bisection method, and the Newton-Rapson method
11. Reviewed procedures for solving a polynomial equation by the factoring method, including zero-product principle and rational root theorem
12. Reviewed procedures for solving a polynomial equation by the bisection method, including intermediate value theorem (IVT) and convergence
13. Reviewed procedures for solving a polynomial equation by the Newton-Raphson method, including quadratic convergence and Taylor linearization
14. Reviewed definition, concepts, notation, terminology, components, and properties of a rational expression
15. Reviewed similarities and differences in the applicability of simplifying a rational expression by the factoring method, the reciprocal method, and the LCD multiplication method
16. Reviewed procedures for simplifying a rational expression by the factoring method
17. Reviewed procedures for simplifying a rational expression by the reciprocal method
18. Reviewed procedures for simplifying a rational expression by the LCD multiplication method
19. Reviewed similarities and differences in the applicability of solving a rational equation by the LCD multiplication method, including checking for extraneous solutions, and the common denominator method, including checking for extraneous solutions
20. Reviewed procedures for solving a rational equation by the LCD multiplication method, including checking for extraneous solutions
21. Reviewed procedures for solving a rational equation by the common denominator method, including checking for extraneous solutions
22. Reviewed procedures for graphing polynomial functions
23. Reviewed procedures for practical interpretation of graphs of polynomial functions
24. Reviewed similarities and differences in the applicability of the polynomial regression model, the polynomial feature engineering technique, and the polynomial interpolation method to a dataset
25. Reviewed definition, concepts, notation, terminology, components, and properties of the polynomial regression model
26. Reviewed procedures for applying the polynomial regression model to a dataset, including methods for choosing the polynomial degree (forward selection, backward elimination, analysis of variance (ANOVA), and cross-validation) to avoid underfitting or overfitting
27. Reviewed definition, concepts, notation, terminology, components, and properties of the polynomial feature engineering technique
28. Reviewed procedures for applying the polynomial feature engineering technique to a dataset
29. Reviewed definition, concept, notation, terminology, components, and properties of the polynomial interpolation method
30. Reviewed procedures for applying the polynomial interpolation method to a dataset
31. Reviewed procedures for simplifying a polynomial expression by the synthetic division method, including remainder theorem and factor theorem
32. Reviewed procedures for solving a polynomial equation by the synthetic division method, including remainder theorem, factor theorem, and rational root theorem
33. Reviewed procedures for finding and analyzing a polynomial’s roots and multiplicities, including the fundamental theorem of algebra, Descartes’ Rule of Signs, and Vieta’s formulas

Part 1 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, and properties of a polynomial expression

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures for performing operations on a polynomial expression (addition, subtraction, and multiplication).  NOTE: Division will be subsequently studied.

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Part 2 of 10

Goal 1 Statement: Review similarities and differences in the applicability of simplifying a polynomial expression by common factoring methods (greatest common factor (GCF), grouping, trinomial factoring, special case – difference of squares, special case – perfect square trinomial, and special case – sum/difference of cubes)

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures for simplifying a polynomial expression by the factoring method of greatest common factor (GCF)

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review procedures for simplifying a polynomial expression by the factoring method of grouping

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review procedures for simplifying a polynomial expression by the factoring method of trinomial factoring

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review procedures for simplifying a polynomial expression by the special case factoring method of difference of squares

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review procedures for simplifying a polynomial expression by the special case factoring method of perfect square trinomial

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Goal 7 Statement: Review procedures for simplifying a polynomial expression by the special case factoring method of sum/difference of cubes

Goal 7 Plan: Read source materials

Goal 7 Work Product: None

Goal Result: Completed

Part 3 of 10

Goal 1 Statement: Review similarities, differences, and applicability of the procedures for solving a polynomial equation by the factoring method, the bisection method, and the Newton-Rapson method

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures for solving a polynomial equation by the factoring method, including zero-product principle and rational root theorem

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review procedures for solving a polynomial equation by the bisection method, including intermediate value theorem (IVT) and convergence

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review procedures for solving a polynomial equation by the Newton-Raphson method, including quadratic convergence and Taylor linearization  

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Part 4 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, and properties of a rational expression

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review similarities and differences in the applicability of simplifying a rational expression by the factoring method, the reciprocal method, and the LCD multiplication method

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review procedures for simplifying a rational expression by the factoring method

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review procedures for simplifying a rational expression by the reciprocal method

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review procedures for simplifying a rational expression by the LCD multiplication method

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Part 5 of 10

Goal 1 Statement: Review similarities and differences in the applicability of solving a rational equation by the LCD multiplication method, including checking for extraneous solutions, and the common denominator method, including checking for extraneous solutions

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures for solving a rational equation by the LCD multiplication method, including checking for extraneous solutions

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review procedures for solving a rational equation by the common denominator method, including checking for extraneous solutions

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Part 6 of 10

Goal 1 Statement: Review procedures for graphing polynomial functions

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 1 Statement: Review procedures for practical interpretation of graphs of polynomial functions

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Part 7 of 10

Goal 1 Statement: Review similarities and differences in the applicability of the polynomial regression model, the polynomial feature engineering technique, and the polynomial interpolation method to a dataset

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, and properties of the polynomial regression model

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review procedures for applying the polynomial regression model to a dataset, including methods for choosing the polynomial degree (forward selection, backward elimination, analysis of variance (ANOVA), and cross-validation) to avoid underfitting or overfitting

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, and properties of the polynomial feature engineering technique

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review procedures for applying the polynomial feature engineering technique to a dataset

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review definition, concept, notation, terminology, components, and properties of the polynomial interpolation method

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Goal 7 Statement: Review procedures for applying the polynomial interpolation method to a dataset

Goal 7 Plan: Read source materials

Goal 7 Work Product: None

Goal 7 Result: Completed

Part 8 of 10

Goal 1 Statement: Review procedures for simplifying a polynomial expression by the synthetic division method, including remainder theorem and factor theorem

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures for solving a polynomial equation by the synthetic division method, including remainder theorem, factor theorem, and rational root theorem

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Part 9 of 10

Goal 1 Statement: Review procedures for finding and analyzing a polynomial’s roots and multiplicities, including the fundamental theorem of algebra, Descartes’ Rule of Signs, and Vieta’s formulas

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

NOTE: Only 9 parts for these topics