Extension of Synthetic Division and Its Applications

Year 2024, Volume: 7 Issue: 2, 59 - 67, 23.05.2024

Aschale Moges Belay , Snehashish Chakraverty

https://doi.org/10.32323/ujma.1405654

Abstract

This study focused on \enquote{Extension of synthetic division and its applications}. The study was designed to show synthetic division and its extension and to point out the applications of synthetic division and its extension. The study found out that the concepts of polynomial and rational expressions in single variables are basic concepts to deal extension of synthetic division and its applications. Using the preliminary concepts, the concept of synthetic division is extended in this study. Also, the study found out that an extension of synthetic division is used for finding the oblique asymptote of the graph of a rational function, evaluating the integration of some rational functions, representing polynomial expression by factorial function in numerical analysis, and so on.

Keywords

Extension of synthetic division, Polynomial expression, Rational expression, Synthetic division

References

• [1] G. Leinhardt, R. Putnam, R. Hattrup, Analysis of Arithmetic for Mathematics Teaching, Routledge, (2020), available at http://books.google.ie/books?id=0GUPEAAAQBAJ&printsec=frontcover&dq=arithmetic+mathematical+operations&hl=&cd=7&source=gbs_api.
• [2] J. French, Common School Arithmetic, BoD-Books on Demand, (2023), available at http://books.google.ie/books?id=qPLEEAAAQBAJ&printsec=frontcover&dq=dividend+and+divisor&hl=&cd=8&source=gbs_api.
• [3] E. Hulbert, M. Petit, C. Ebby, E. Cunningham, R. Laird, A Focus on Multiplication and Division, Taylor and Francis, (2023), available at http://books.google.ie/books?id=9Fi-EAAAQBAJ&printsec=frontcover&dq=purpose+of+mathematical+division&hl=&cd=2&source=gbs_api.
• [4] J. Midthun, Division, World Book, (2022), available at http://books.google.ie/books?id=spuczwEACAAJ&dq=purpose+of+mathematical+division&hl=&cd=1&source=gbs_api.
• [5] E. Berkove, M. Brilleslyper, Summation formulas, generating functions, and polynomial division, Math. Mag., 95(5) (2022), 509–519, available at https://doi.org/10.1080/0025570x.2022.2127302.
• [6] F. Laudano, Remainder and quotient without polynomial long division, Internat. J. Math. Ed. Sci. Tech., 52(7) (2020), 1113–1123, available at https://doi.org/10.1080/0020739x.2020.1821108.
• [7] J. Abramson, College Algebra, (2018), available at http://books.google.ie/books?id=hGGatAEACAAJ&dq=polynomial+and+rational+functions&hl=&cd=3&source=gbs_api.
• [8] E. Gselmann, M. Iqbal, Monomial functions, normal polynomials and polynomial equations, Aequationes Math., 29 (2023), 1059–1082, available at https://doi.org/10.1007/s00010-023-00972-z.
• [9] A. Dubickas, Shifted power of a polynomial with integral roots, Math. Slovaca, 73(4) (2023), 883–886, available at https://doi.org/10.1515/ms-2023-0065.
• [10] S. MacLane, G. Birkhoff, Algebra, Amer. Math. Soc., (2023), available at http://books.google.ie/books?id=wQvfEAAAQBAJ&pg=PA280&dq=Linear+factorization+theorem+for+plynomial&hl=&cd=6&source=gbs_api.
• [11] I. Qasim, Refinement of some Bernstein type inequalities for rational functions, Issues of Anal., 29(1) (2022), 122–132, available at https://doi.org/10.15393/j3.art.2022.11350.
• [12] P. Aluffi, Algebra: Chapter 0, Amer. Math. Soc., (2021), available at http://books.google.ie/books?id=h4dNEAAAQBAJ&printsec=frontcover&dq=polynomial+division+theorem&hl=&cd=9&source=gbs_api.
• [13] Y. Kim, B. Lee, Partial fraction decomposition by repeated synthetic division, American Journal of Computational Mathematics, 06(02) (2016), 153–158, available at https://doi.org/10.4236/ajcm.2016.62016.
• [14] M. Mohajerani, Division of Polynomials, (2020), available at http://books.google.ie/books?id=XHc9zgEACAAJ&dq=synthetic+divisions+for+polynomial&hl=&cd=1&source=gbs_api.
• [15] L. Marecek, M. AnthonySmith, A. Mathis, Intermediate Algebra 2e, (2020), available at http://books.google.ie/books?id=8dEGzgEACAAJ&dq=synthetic+divisions+for+polynomial&hl=&cd=4&source=gbs_api.