Add to ORKGSomewhere at a casino, a person is rolling two six-sided dice and adding the values of the top faces. Out of 36 outcomes, both snake-eyes (1+1=2) and boxcars (6+6=12) can occur in exactly one way, while 7 can occur in six ways. Note that the distribution for the sums 2 to 12 is 1 2 3 4 5 6 5 4 3 2 1. Next, note that (x^1+x^2+x^3+x^4+x^5+x^6) = x^2+2x^3+3x^4+4x^5+5x^6+6x^7+5x^8+4x^9+3x^10+2x^11+x^12. The sum of the dice and products of the polynomials are equivalent, due to the addition property of exponents. Does a different set of dice produce the same distribution? Yes: dice labeled (1 2 2 3 3 4) and (1 3 4 5 6 8) correspond to the factorization (x^1+x^3+x^4+x^5+x^6+x^8). In this Demonstration, polynomial factorization is used to find all...