Problem Statement

Let us suppose a polynomial is represented by a vector,

x

{\displaystyle x}

(i.e., an ordered collection of coefficients) so that the

i

{\displaystyle i}

th element keeps the coefficient of

x

i

{\displaystyle x^{i}}

, and the multiplication by a monomial is a shift of the vector's elements "towards right" (injecting ones from left) followed by a multiplication of each element by the coefficient of the monomial. Then a pseudocode for the polynomial long division using the conventions described above could be: Note: vector * scalar multiplies each element of the vector by the scalar; vectorA - vectorB subtracts each element of the vectorB from the element of the vectorA with "the same index". The vectors in the pseudocode are zero-based.

Example for clarification

This example is from Wikipedia, but changed to show how the given pseudocode works.

Let's start with the solution: