When I teach multiplying binomials, I teach five different methods because many of my students do not relate to the FOIL method. They sometimes ask "How do I use this in real life"? and I have no answer for it. When I got my degree in math (Yes I'm one of those weird ones) I specialized in theoretical math and never bothered learning real life applications for what I learned. Unfortunately, most of my students always want to know why they need it.

Multiplying binomials and factoring polynomials go hand in hand, so when discussing multiplying binomials, you have to discuss factoring polynomials and the same question arises with factoring polynomials. "How is this used in real life"? Its going to be on the test will stop their questions but it doesn't satisfy their desire to know why its important to learn the material.

This prezi has some nice examples to answer this question. It covers dropped balls, architecture, and painting. Its short and sweet but a nice introduction. On the other hand, Mathematics Stack Exchange has a great answer that explains its use in engineering. This PDF has three really nice examples including one that looks at accidentally dropping a camera off a bridge into the water. That is one that I have seen happen in real life when someone was taking a picture of something and a bee came bye and surprised her. There went the camera.

This site gives a list of occupations which require people to factor polynomials. The list has 31 jobs including Funeral Directors! There are several jobs on the list I'm not familiar with. I assume you could easily check the site for other mathematical topics to see which jobs use them. This list is a great starting point to look up the individual job to find out how they use polynomials. I looked up funeral directors + polynomials and came up with this prezi that talks about cost of multiple funerals and includes three other areas.

Math is Fun has the best real world examples I've seen for factoring polynomials. They give a situation and they show the math to prove how factoring is used. One example is designed to tell how high you threw the ball, two examples focus on selling items, one example even discusses resistors in parallel. I like the variety of examples shown and the fact they include the mathematics.

I think I am better prepared to answer the questions from students on "Who uses this?" I am always glad to be able to answer something other than you need it to graduate or for the next high stakes test.