What is Factoring? 03:48 minutes

Video Transcript

Transcript What is Factoring?

This is the year for Planet X to host the annual Confederation of United Planets, better known as CUP. The invitations have been sent out by spaceship which will soon return filled with aliens from many different planets. Everything is almost ready, but Ralph Kakerlake is still finishing his work. He's deciding on some activities the aliens can do during their free time. To keep everything fair, he'll have to use factoring to decide on the program. But, what is factoring? First, Ralph wants to build interplanetary relations by holding a sports tournament where each team is made up of aliens from different planets. Ralph wants to make sure each team has the same number of players. The number of players per team will determine which sports they can play. Ralph knows each spaceship holds 12 aliens. Unfortunately, he doesn’t know how many planets will accept the invitation. Since he's not sure how many planets will send back spaceships, let’s use the variable 'x' to represent the number of spaceships that return. Ralph also has to include the 66 ambassadors from the host planet. Therefore, the number of participants will be 12x plus 66. Now that Ralph has an expression representing the number of participants, he wants to divide these aliens into groups of equal size. This way, he’ll know which sports they can play. In order to divide the aliens into groups of equal size, Ralph will have to use factoring. First, Ralph has to look for the greatest common factor, or GCF, of 12x and 66. In this case, it's 6. This is the largest number that goes evenly into both 12 and 66. Therefore, we can factor a 6 out of the expression. The expression becomes 6 times the quantity 2x plus 11. You can think about this as reverse distribution because if you were to distribute the 6 to the 2x plus 11, you would get the original expression, 12x plus 66. Since 6 can be factored out of the expression, this means that no matter how many planets accept the invitation, they can always split the aliens into equal groups of 6. That's perfect for playing slamball, which is similar to the basketball they play on Earth. After playing slamball, Ralph wants to set up a special 3 on 3 slamball tournament. But how big should the groups be? Ralph decides to only let the senior ambassadors perform in this exclusive event. This means that there will be 6 participants from each planet that accepts the invitation, plus 15 members from the host planet. He can represent this using the expression 6x+15, where x is still the unknown number of planet that will accept the invitation. Ralph wants to split these members in to groups of equal size. He realizes that he can factor a 3 out of the expression 6x+15, because 3 goes evenly into both 6 and 15. After factoring out 3, the expression becomes 3 times 2x plus 5. This means that no matter how many planets accept the invitation, they will be able to split the aliens into groups of 3. All of the spaceships have arrived to Planet X, and it looks like every planet sent their 12 representatives. Ralph's math was correct, so he randomly divides the aliens into teams of 6 for slamball and groups of 3 for the special tournament. They start off with slamball. As the teams are formed, Ralph realizes that even though his math was right, it looks like the teams might be a little uneven. Not all aliens have the same talents...