Polynomial long division is an algorithm. By that I roughly mean that it is an entirely mechanical procedure that is guaranteed to finish in finitely many steps. In order to ensure this, we want a …

Jan 6, 2015 · I get normal long division but this doesn't make sense. How can doing it by only dividing by the leading term work? The problem is $$\dfrac {3x^3 - 2x^2 + 4x - 3 } {x^2 + 3x + …

Mar 18, 2021 · In long division, we have to pay attention to the entire divisor because multiples of the divisor can result in carries between the various digits (columns in the usual tableau for …

Feb 19, 2014 · It looks like you are XORring as opposed to subtracting. This means that you are doing long division in the ring of polynomials of binary coefficients ($\Bbb {F}_2 [x]$). This is …

2 I am solving a differential equation which requires solving and integrating $ (4y^3 + 10y^2 + 5y + 2) / (2y^3 + 3y^2 + 3y + 1)$. I am thinking synthetic division to reduce it but am not sure where …

21 No, the polynomial division algorithm does not immediately generalize to multivariate rings. Here is a simple proof. Just as for $\rm\:\Bbb Z,\:$ a domain having an algorithm for division …

Jan 28, 2020 · Why must you do polynomial long division to find oblique asymptotes of rational functions? Ask Question Asked 5 years, 9 months ago Modified 4 years, 2 months ago

Synthetic division is simply the polynomial long division algorithm optimized for a linear divisor. Said Wikipedia pages both do the same example. Put both pages side-by-side and it should …

Feb 8, 2021 · I would like to understand the mathematics behind the standard long division algorithm, specifically for the ring of $\\mathbb{Z}$. I'm looking for an algebraic or set theoretic …

Jan 1, 2012 · The key idea of polynomial division is this: if the divisor has invertible lead coef $\,b\,$ (e.g. $\,b=1)\,$ and the dividend has degree $\ge$ the divisor, then we can $\rm\color …