Factoring polynomials in 

real life   

Quadratics do play a role, for example, in area and construction problems.

Example: Suppose that you were told that a piece of land had a width that was 15 feet wider than its length, and that the area was 5800 square feet.

With that problem, you'll be ending up solving the equation  or further worked out,  which you would need to factor to get . 

Suppose that you have a bus, and you're renting it to organizations. Your bus can seat 80 people. You decide to charge the first person $30.00. If that person brings another person, you charge both of them $29.75 each. If there are three people, you charge $29.50 each. In other words, You charge EVERYBODY $0.25 less for every person who joins in. The thing is, there will come a point when you've got enough people to ride that you'll start losing profit if you add more people to the deal. With your starting price and discount price per additional person, will you: A) maximize your profit on the 80th person who rides? B) Be losing profit before you fill your bus, or C) would not yet reach your maximum profit on the 80th passenger?

So the total charge is dependent on how many people there are, how much you charge them, and what type of incentive you give depending on how many people there are. So, if there's one person, your total profit is $30.00. If there are two people, that's 2 people * ($30.00 - 0.25(1)). If there's 3 people, your total charge would be 3 people * ($30.00 - 0.25(2)).... Pretty soon, you'll see that your profit will be  or if simplified,