Polynomials — Division by Vision with Remainders (Part A)

A fresh way to apply ‘division by vision’ in higher order polynomials with quadratic quotients with remainders, while saving time.

In my post Polynomials — Division by Vision, I presented a further method for dividing higher order polynomials, without long division.

I call the approach ‘division by vision’ as it helps you to ‘visualise’ the outcome of the equation. The main advantage of ‘division by vision’ is its speed, and less chance of errors (in absence of a calculator).

While useful in many applications, the method, derived from my original polynomial factoring post, Polynomial Division — by Formula, was limited to division resulting in quadratic quotients without remainders.

Here in Part (A) of a two part series, I remedy that restriction by introducing a simple method for ‘division by vision’ to determine linear x and constant term remainders.

Part B (coming shortly) covers polynomial division with higher order cubic quotients and non-unity first coefficients.

I think the methodology for finding remainders is simple enough to still qualify as ‘division by vision’. Hopefully you will agree!

This post assumes knowledge of algebra at the high school level.

The Foundations

Before we go into the new method, if you would like a detailed understanding of the underlying math, you can visit two of my earlier…