I recently completed the videos based on my guest article on Numerical and Polynomial Synthetic Division. The playlist includes both full-length videos and shorts. All related to my discovery or rediscovery of numerical synthetic division.
Article Link
Video Playlist
Outline of Video series- Ep 1. Numerical and Polynomial Synthetic Division Article
- Overview of the guest article
- An example of polynomial synthetic division
- An example of numerical synthetic division
- Ep 2. Introducing Negative Digits
- Negative digits are used with numerical synthetic division
- What they are
- How to convert our numbers and numbers with mixed digits
- Ep 3. Vedic Division
- Similar, but limited to synthetic division
- Two styles of Vedic division
- Ep 4. Extended Form of Polynomial Synthetic Division
- Examples showing synthetic division can be used with any polynomial
- "Remove and replace" property of synthetic division
- Note: different from most (or all) textbooks
- Ep 5. Numerical Synthetic Division
- 26,763 divided by 58
- Same division problem, shown through 3 different ways
- Ep 6. More Examples of Numerical Synthetic Division
- Ex1. 8889÷37
- Ex2. 999,999÷285
- Ex3. 34568÷7825
- Ep 7. Verifying Irrational and Complex Zeros with Synthetic Division
- Ex1. Check if 1 ± √5 are zeros of 2𝑥^3 − 5𝑥^2 − 6𝑥 + 4
- Ex2. Check if 1 + √5 is a zero of 2𝑥^3 − 5𝑥^2 − 6𝑥 + 4
- Ex3. Verify that −2 + 3𝑖 is a solution of 𝑥^2 + 4𝑥 + 13
- Ep 8. Synthetic Division of Multivariable Polynomials
- Ex1. (6𝑥^4−7𝑥^3 𝑦+5𝑥^2 𝑦^2+7𝑥𝑦^3−11𝑦^4)÷(3𝑥^2−2𝑥𝑦+3𝑦^2)
- Ex2. (𝑥^2+2𝑥^2 𝑦−2𝑥𝑦+4𝑥𝑦^2−3𝑦^2)÷(𝑥+𝑦)
Ep 1 gives an overview of the article. Ep. 2-4 gives the foundation for the discovery of numerical synthetic division. Ep 5-6 introduce numerical synthetic division and demonstrate the algorithm with various examples. Ep 7-8 discuss interesting ways synthetic division can be used, based on Ep 4.
In the future, I may produce more videos related to synthetic division as I research other ways in which polynomial and numerical synthetic division can be used.
