Factoring is one of techniques that is used most in your later mathematics classes, and you will find that it shows up in a wide variety of different topics. One of the most common uses of factoring is in solving equations. It is based on the following simple idea, which is called the Zero Product Rule:
Zero Product Rule. If several things are multiplied, and the result is zero, then at least one of the original things must be zero.
This rule allows us to take a more complicated equation and, after factoring, split it up into several simpler equations. This video shows the final steps of the process, starting with an equation that is already factored:
Of course, the equation will usually not be factored for you — you will need to factor it first, and then follow the steps as above.
Applications. There are a number of applications that use these ideas. I will provide a few different examples here.
Example 1: There are three consecutive integers. The product of the two larger integers is 30. Find the three integers.
Example 2: A rectangular building is to be placed on a lot that measures 30m by 40m. The building must be placed in the lot so that the width of the lawn is the same on all four sides of the building. Local restrictions state that the building cannot occupy any more than 50% of the property. What are the dimensions of the largest building that can be built on the property?