Polynomials — Division by Vision

Using vision for division of higher-order polynomials, without formulas or long division.

This post complements my recent post, Polynomial Division — by formula which presented a method for dividing higher order polynomials, without long division.

That method and this new approach is limited to division resulting in quadratic quotients without remainders.

The earlier version presented results in factor notation. This method presents in the usual ax²+bx+c quadratic form.

The earlier Polynomial Division — by formula method uses a variant of the Quadratic Equation in my post, Cubic Polynomials — A Simpler Approach.

The modified equations bridged the need for polynomial division in finding quotient factors.

This new post expands on that methodology’s understanding of the architecture of polynomials to present a one-line answer by vision without long division.

This method is for polynomial division resulting in quadratic quotients, but with a simple adaptation it can be used to generate that outcome with a particular non-compliant numerator.

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