3 things I learned this semester thus far:

The number in front the square root sign is the coefficient, the small number connected to the square root is the index and the number inside is called the radicand. We learned that the index is a very important clue for the equations because it tells us is the number in the radicand spot can me both negative and positive or only positive. Even number index can only be positive while uneven index can be either. Also simplifying equations, the index is important because it tells us what we can take out to become the coefficient. if the index is 2 we take groups of two.

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.

completing the square-

probably the most complicated way to factor in my option because in order to do this process you need to move the third term and bracket the first 2. Then half the square the second term, the one inside the bracket will be positive and then one outside the bracket will be negative. Keep in mind if the first term has a coeficial you have to times the number by the coeficiant outside the bracket. To made this more clear I will show you a photo below.