#1
Matlab is not a symbolic computing environment, and as such, you cannot "divide polynomials." But you're in luck: polynomials can be manipulated in Matlab as a vector of coefficients.
For example, the vector [1 0 1] is x^2 + 1. The vector [a b] is ax+b for any numbers a and b. I hope that explains it well enough. Multiplication of these vectors is called a convolution. Division is a deconvolution.
So the commands are:
p=[2 -3 0 -5 3 -2];
q=[2 1 -1];
[a b] = deconv(p,q);
Note that the first polynomial is not divisible by the second. The "whole" part is stored in the vector a, the remainder is left in the vector b. a represents a 4th degree polynomial, while b represents a linear one. The answer to the division is of the form a + b/q, like any other division-with-remainder problem.
#2
To solve the roots of a polynomial, there's a simple command.
p = [16 22 -15];
r = roots(p)
#3
Here we have to use a little bit of Matrix theory. Again, Matlab is not a symbolic computational environment, it's a numerical one. We make a coefficient matrix, a constant vector, and do the matrix division. Note that the constant vector is a column, as is the output vector X = [x ; y]
A = [3 2;9 -8];
b = [3; 2];
X = A\b
Note that you have to divide by A on the left (and use a backslash instead of a slash). For matrices, division and multiplication are not commutative, so be careful.
However, I will again note that this is not a symbolic computing environment, and for some of these things, you might find a symbolic environment (e.g. Mathematica) much easier. See: http://wolfram.com/ . In Mathematica, these problems would be much simpler and intuitive:
#1
(2*x^5-3*x^4-5*x^2+3*x-2) / (2*x^2+x-1)
#2
Solve[16x^2+22x-15==0]
#3
Solve[ {3x+2y == 3 , 9x-8y == -2} ]