Use the interactivity to experiment. Start with $2$ spinners
labelled $1, 2, 3$ and $4$. Then each spinner is represented by the
polynomial $x + x^2 + x^3 + x^4$. The computer will model your
experiment by randomly choosing one number from each spinner and
recording the sum of the two numbers. Repeat the experiment enough
times for the freqency distribution of the scores to be close to
the theoretical distribution.

Look at the coefficients when you have expanded the polynomial $(x + x^2 + x^3 + x^4)^2$ and compare them to the relative frequencies in which the different possible scores occur.

Now combine the factors of the polynomial in different ways. In each polynomial factor the powers correspond to the labels on the spinners so that different factorisations correspond to different labelings of the spinners.

Now do a computer experiment with spinners with the new labelling.

Because the expanded polynomial is the same the differently labelled spinners will produce scores with the SAME relative frequencies. Try it out.

Look at the coefficients when you have expanded the polynomial $(x + x^2 + x^3 + x^4)^2$ and compare them to the relative frequencies in which the different possible scores occur.

Now combine the factors of the polynomial in different ways. In each polynomial factor the powers correspond to the labels on the spinners so that different factorisations correspond to different labelings of the spinners.

Now do a computer experiment with spinners with the new labelling.

Because the expanded polynomial is the same the differently labelled spinners will produce scores with the SAME relative frequencies. Try it out.