Polynomial long division script writing

I'm trying to write a code for polynomial long division, for vectors P divided by Q to give remainder R and equation S.

clear all; clc

P = [1 -5 3 -15]

Q = [1 0 3]

lengthQ = length(Q);

i = (length(P)-length(Q))+1;

while i>0

% Making Q the same length as P

diff_length = length(P)-length(Q);

QlengthP = [Q (zeros(1, diff_length))];

% Take the first number from Q and divide the first number from P by this.

Xone = P(1,1)/Q(1,1);

% Multiplying the Q by the divised

for_sub_or_add = Xone*QlengthP

% Deciding whether to subtract or divide

    if sign(P(1,1)) == sign(for_sub_or_add(1,1))

        P = P - for_sub_or_add

    elseif sign(P(1,1)) ~= sign(for_sub_or_add(1,1))

        P = P + for_sub_or_add

    end

P = P(find(P ~= 0))

Q = for_sub_or_add(find(for_sub_or_add ~= 0))

i = i-1

end

But it just won't work! I know there are short cuts of doing this but i'm not allowed to use those!

Please help, im at my wits end now!

thanks