How can you use solving by factoring in real life applications?

Priscilla

If you are asking about factoring integers, we do it quite often. Seven children came to my daughter's birthday party and I have twenty-eight treats I can hand out. Since I know that twenty-eight factors as

28 = 4 7,

I expect however that you are asking about factoring algebraic expressions. I am a university mathematics professor and I use factoring every day. I expect that other mathematicians and mathematics teachers do so also. People in many other professions who use mathematics in their jobs, such as scientists and Engineers would also use factoring quite often.

I see factoring as an exercise in "pattern recognition", that is looking at an expression and seeing a pattern, or something familiar that makes you think "this is probably a difference of squares". It's like hearing the first three notes of a song and recognizing right away what song it is. This is a very valuable ability to have, to be able to "see" patterns. Much of our skill in dealing with new situations depends on our ability to quickly categorize what is similar to things we have seen before, and then focus on what is really new. I believe that any activity that enhances our skill in recognizing patterns, like factoring, or studying ballet, or learning to play the piano, or reading the opposition's defence, increases our ability to function in the "real world" in an intelligent way.