Factoring is often a key skill for solving problems in which you need to find a value for x. What can x equal in real life? Well, about anything. Being able to solve for x is the foundation of algebra, which itself is the foundation for doing trigonometry and calculus and higher math. Want some examples?
Well, suppose you would like to own a business one day. Say you own a painting company and have several employees. You get a rush job to paint a large hotel conference room. Knowing from experience how fast your employees work, you know that Joe can do a room this size in twelve hours, Max can do the job in nine, and Jane can do the job in ten and a half. How long should it take them, then, to do the whole job if you let them work together? To figure this out you need to be able to factor. Only if you know the answer to this question will you be able to tell if they are working hard for you or taking advantage of your mathematical ignorance.
Suppose you want to sell a product, such as mixed nuts. What is the ideal size of box or can for the quantity of product you want to sell? After all, cardboard and metal costs money, and storage of overly large containers wastes cash. To find the ideal size, you will need to be able to factor.
Those nuts you want to mix; prices on nuts change all the time. One day the cost of peanuts may be up, or on another day walnuts may be down. How should you tweak the mix to hold the price you charge constant as the various nut prices change? To figure that out, you will need to know about factoring.
Suppose you want to make computer games which play dice, or launch birds; or perhaps you want to write a program to keep data secure or do scientific research which tracks how owl populations change in relation to weather patterns. To figure all of these things out, you will need to know about factoring.
Factoring is your gateway to doing big things in life. If you want be a chemist or astronomer or ecologist or physicist, or programer or be your own boss and have a competitive edge, or do anything beyond working the 9-to-5; if you want to be a leader in your field and do big things, you will need skills in mathematics which are built upon college algebra, and for that you need to learn about factoring. That is why these skills are important. Those who have math skills earn more money. That is why you should learn about Algebra. That is why you should learn about factoring.
On reflection I realize that a couple of my examples (I will not share which ones) can be figured without factoring because they are linear in nature rather than involving a changing curve. In grade school you learn about math which deals with lines, and you can do quite a bit in life with just those skills. But not everything in life is linear, and to go beyond life-on-a-line, to go beyond grade-school understandings and grade-school skills, to be more, do more and understand more, you need math which can handle change and curves.
There is a secret you can use to stand out in the adult job world, and you don't even have to be particularly gifted at math to take advantage of it. Most people give up learning math the moment they can, and never go beyond whatever math they were required to take in grade school or college. Worse yet, they almost never practice what they did learn. Their failure is your opportunity to get ahead.
The secret is this: Don't stop. Keep learning, keep studying, keep practicing math even when you are out of school and you will leave those who do give it up in the dust. Math isn't something you can cram for, like a quiz or history test. Math isn't something you can fake. Math is like learning to play a musical instrument. It takes practice. Do what you find to be fun, yes, but keep challenging yourself, keep learning and keep pushing ahead.
Even if you never need to know how long a toy rocket should wait to deploy its chute so as to have the longest trip to the ground, the day will come when one of your kids will want your help with factoring; and wouldn't you like to be able to show them how? Math is worthwhile for its own sake; a game which can be played when all you have is a pencil and paper and half an hour to kill. Don't waste those minutes staring at a wall. Math can be fun!
Here is a parting challenge. Which examples in my original post can be calculated using just the math of straight lines (using grade-school math and simple algebra), and which of them require factoring to solve because they are problems about curves intersecting a y = 0 x-axis line? Do you know enough about factoring to say? Wouldn't you like to?