Here are the calculations for the product of A, B, and C with s.

Now, A . s * B . s — C . s:

t = [-88.0, 592.666, -1063.777, 805.833, -294.777, 51.5, -3.444]

The result is obtained by expanding as polynomials and operating on them, not by operating on the matrices, as is done here.

Z = [24, -50, 35, -10, 1]

That result is here.

h = t / Z = [-3.666, 17.055, -3.444]

I was able to get this result as a Taylor Series on a Wolfram Alpha widget.

To get the result you can use these values:

(-(3+4/9)*x⁶+51.5*x⁵-(294+7/9)*x⁴+(805+5/6)*x³-(1063+7/9)*x²+(592+2/3)*x-88)/((x-1)(x-2)(x-3)(x-4))

Or:

(-(3+4/9)*x⁶+51.5*x⁵-(294+7/9)*x⁴+(805+5/6)*x³-(1063+7/9)*x²+(592+2/3)*x-88)/(x⁴-10x³+35x²-50x+24)

Or:

P(x) = (-(3+4/9)*x⁶+51.5*x⁵-(294+7/9)*x⁴+(805+5/6)*x³-(1063+7/9)*x²+(592+2/3)*x-88)

Q(x) = (x⁴-10x³+35x²-50x+24)