Polynomial division - quotients Q and remainder R

I want to divide two polynomials (numerator and denominator). The result should be displayed as quotients Q and remainder R. Like here:

Result:

Matlab code

clear all;
close all;
clc;

syms x

I_sym = x^7 + x^3 + x^2 + x;

G_sym = x^4 + x^3 + x^2 + 1;

xK_sym = x^4;

%% Convert to polynomial
I_pol = sym2poly(I_sym);
G_pol = sym2poly(G_sym);
xK_pol = sym2poly(xK_sym);

Numerator = conv(xK_pol, I_pol);
Denominator = G_pol;

[Q, R] = deconv(Numerator, Denominator)

The result looks like this:

Q =

     1    -1     0     1    -1     2     0    -3


R =

     0     0     0     0     0     0     0     0     4     1     0     3

This is not the expected result. What have I done wrong?

Answer 1

[Pratheek Punchathody]

Looks like you have obtained the right quotient and remainder for the above two polynomials. Even using the direct co-efficients of the polyomials with the "deconv" function, the mentioned results are obtained.

u = [1 0 0 0 1 1 1 0 0 0 0 0];
v = [1 1 1 0 1];
[q,r] = deconv(u,v);

Results:

q =

     1    -1     0     1    -1     2     0    -3

r =

     0     0     0     0     0     0     0     0     4     1     0     3