Week 5 – Pre-Calc 11

Hello! This week was an interesting one. With having a unit test and all that jazz. One concept that stuck with me was factoring and the acronym CDPUE. Can Divers Pee Underwater Easily. Well, that’s just a way to remember it but the real meaning is Common, Difference of Squares, Pattern, Easy, Ugly.

These terms refer to what “kind” of factoring must be done and makes the whole process much easier.

First off we have common. This refers to the fact we can take a common number out and turn it into a coefficient.

Ex: =

Second, there is a difference of squares which pretty much sums up what it means. If there are two perfect squares, we can make a conjugate. * Remember that a conjugate is to of the same terms one positive and one negative*

Ex: =

Third comes a pattern which happens whenever there is a an and a number.

Ex: =

Fourth there is easy which is when you can use the product and sum to easily determine the factored result.

Ex: =

(6+2 = 8 which is the sum and 6×2 = 12 which is the product)

Finally, we have the ugly duckling. This is no fun and requires you to make a square to solve. Since I can’t physically make a square on this blog, ill describe it as best as I can.

Ex: =

To solve this you would make a square with four quadrants. In the top left you would put the and in the bottom right, you would put the 12. Multiply the two together to get a product. Then find out all the ways of multiplication to reach that product. Find the one that adds up to a sum of your other number. It doesn’t really matter where the numbers go in the square. *If there is no product that makes a correct sum, there may not be a solution*

Once you are done that, factor out what you can and put the two numbers into brackets to factor!

Essentially this is a backward multiplication square.

That’s all and thanks for checking it out.