Why Is It Important To Teach Long Division For Dividing Polynomials.

 

This is one of those topics I really hate teaching, especially right now because most students have difficulty doing regular long division.  This has become even more apparent due to COVID and I have so many students who cannot divide without a calculator.  Although there is a wonderful shorter method referred to as synthetic division but it only works in specific situations.  

What I've learned over the years is hat if a student struggles with regular long division, they struggle with polynomial long division due to the process being the same. So when teaching this topic, it may be necessary to backtrack all the way to regular long division.

There are many reasons for students to learn long division with polynomials.  First, since division is a fundamental operation, teaching them to divide polynomials is helping them to apply the algorithm to algebraic expressions. Understanding this is essential for higher mathematics classes such as calculus and Complete factorization is important for solving equations, finding roots, and simplifying expressions. 

Next, being able to divide polynomials by using long division is essential to  factoring polynomials because it is a systematic approach that can be used in multiple situations.  The long division algorithm provides a step by step method for dividing polynomials while reinforcing algorithmic thinking.  It also helps reinforce problem solving skills for the more complex problems.  

As far as problem solving goes, long division requires careful organization and attention to details. It encourages logical thinking,  The process has students analyze the problem, break it down into smaller steps, and apply the appropriate strategies to find the quotient and remainder.  These skills are transferable and can be used in other math courses and in real life.

It also provides a foundation for higher level mathematics. In addition, it is the foundation of other mathematical topics such as synthetic division.  Of course, students will ask "When are we going to use this?" Or "When is it used in real life."  This is fairly easy to answer. 

Polynomial long division is used in circuit analysis when they are analyzing electrical circuits with complex transfer points or calculating the stability of a system by diving the input by the output. Another place is in control systems to determine the stability of feedback systems. In economics, polynomial division to determine roots and critical point used to understand market equilibrium and economic behavior.  In data interpolation, one use is to determine missing points and values within a data set. Furthermore, it is used in error correction codes such as the Reed Solomon codes which help detect and correct data transmission or storage systems. 

Although students will argue why learn since there are calculators out there that will do it for them, it is still important for them to learn the process so they understand how it works.  Let me know what you think, I'd love to hear.  Have a great day.