How can I expand polynomials with matlab?

Can matlab expand something like the following and represent it in terms of powers of 'x'?

x(x-7)(x-6) + (x+4)(x-9)(x-2) + x(x-8)(x+1) ----> k_1 x^3 + k_2 x^2 + k_3 x + k_4

[Star Strider]

It can if you have the Symbolic Math Toolbox.

Answer 1

[John D'Errico]

Trivial. With or without the symbolic toolbox. First, with...

syms x
P = expand(x*(x - 7)*(x - 6) + (x + 4)*(x - 9)*(x - 2) + x*(x - 8)*(x + 1))
P =
3*x^3 - 27*x^2 + 8*x + 72

Without the symbolic toobox, but with my sympoly toolbox , as found on the file exchange. Its free, but less capable than the symbolic one.

sympoly x
P = x*(x - 7)*(x - 6) + (x + 4)*(x - 9)*(x - 2) + x*(x - 8)*(x + 1)
P =
    72 + 8*x - 27*x^2 + 3*x^3

In either case, it is easy enough to extract the numeric coefficients alone, if that is what you wanted.

And if you have neither toolbox and you like to do your own work (hey the sympoly toolbox is FREE after all)

coef = conv(conv([1 0],[1 -7]),[1 -6]) + ...
       conv(conv([1 4],[1 -9]),[1 -2]) + ...
       conv(conv([1 0],[1 -8]),[1 1])

coef =
   3   -27     8    72

Answer 2

[Star Strider]

An alternative using poly (assuming I got the maths correct) is:

% f(x) = x(x-7)(x-6) + (x+4)(x-9)(x-2) + x(x-8)(x+1) 
rts1 = [ 0  7  6];
rts2 = [-4  9  2];
rts3 = [ 0  8 -1];

trm1 = poly(rts1);
trm2 = poly(rts2);
trm3 = poly(rts3);

ply = trm1 + trm2 + trm3;

produces:

ply =

       3    -27     8    72