What is a real world application of polynomial factoring? The wife and I are sitting here on a Saturday night doing some algebra homework.  We're factoring polynomials and had the same thought at the same time: when will we use this?
I feel a bit silly because it always bugged me when people asked that in grade school.  However, we're both working professionals (I'm a programmer, she's a photographer) and I can't recall ever considering polynomial factoring as a solution to the problem I was solving.
Are there real world applications where factoring polynomials leads to  solutions? or is it a stepping-stone math that will open my mind to more elaborate solutions that I actually will use?
Thanks for taking the time!

If one has a 2x2 two-person zero-sum matrix game M (where neither row dominates the other, nor column dominates the other) where Row can play row I or II and Column can play column 1 or 2, what is the optimal mixed strategy for each player? If Row plays Row I with probability p and Row II with probability 1-p and Column plays Column 1 with probability q and Column 2 with probability 1-q then one can compute the expected value from Row's point of view. This expected value is a polynomial in p and q (and constants from the matrix M). One can factor this polynomial into the form C(p-s)(q-t) + V. V is the value of the game (from Row's point of view) and s and t are the optimal mixed strategies and C is a constant. The beautiful result is that if Row plays optimally (p = s) then whatever Column does not matter (similarly reasoning for Column about what Row does), since the term (p-s)(q-t) will be 0. So if V is positive Row can get a gain of V on average with each play of the game in the long run. (When V is negative the game is "biased" towards Column; when V is 0 the game is fair.) if Column wants to keep losses to a minimum (V positive case) the optimal play is q = t. This is not a "standard" high school factoring problem but it is a very nifty way to see a not obvious lovely result by factoring a polynomial.
