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!

You need polynomial factoring (or what's the same, root finding) for  higher mathematics. For example, when you are looking for the eigenvalues of a matrix, they appear as the roots of a polynomial, the "characteristic equation".
I suspect that none of this will be of any use to someone unless they continue their mathematical education at least to the junior classes like linear algebra (which deals with matrices) and differential equations (where polynomials also appear). And I would also bet that the majority of people who take these classes never end up using them in "real life".
