This week in PreCalc 11, we learnt about factoring polynomials. To factor a polynomial, we have to go through certain steps to find the answer or solution. To remember this we use the acronym CPDEU, to remember this we use Can Divers Pee Easily Underwater.

Common Factors

Difference of Squares

Pattern

Easy

Ugly

C- Common Factor is when we look to find if the trinominal has something in common and if it does we will take it out so it makes our trinominal look more simple and easier to factor. For example in the picture below we need to recognize that we can take out a common factor of 3.

D- Différence In squares we need to see 3 things. Is it a binomial, is the refond term negative and, are they both perfect squares. If all of these are yes then we can factor it quite easily like in the example below.

P- Pattern is probably the easiest one because we are just checking if it has the right structure, and if it is then it is most likely facorable. Does it have X squared, does it have an X term and a number at the end. If yes then you can proceed to the next step.

E- Easy means if it is a easy polynomial to factor as in is does the X squared have a coefficient of 1. If it does this will be easy. Don’t stress until they are ugly.

U- Ugly is the opposite of easy (of course) which means that is the X squared has a coeficcisnt of 2 or more then it is considered ugly and you’ll have to do a bit more thinking.