Different types of factoring

There are 4 major different types of Factoring

which are called

+Common Factoring

+Difference of a Square

+Simple Trinomial

+Complex Trinomial

The first one is the basic you learn this in elementary school. An example of this is:

5x2 - 15x

To Solve it would be:

5x2 - 15x

5x(x-3)

5x= 0

5x/5=0/5 *Note / means divide

x=0

The Second is Difference of Square an example of this one: Btw for this factor u need to Set Each Factor to 0

x2 -49=0

(x+7)(x-7)=0

x+7=0 OR x-7=0

x=-7 x=+7

The Third is Simple Trinomial Factoring which is alittle bit tricky here's an example:

x2-2x-15=0 Now for this factoring you need to find what two numbers mulitply with the last term( ur c value its -15) and adds to the middle term (ur b value its -2x)

So the best way to figure this out is to do this trick find all numbers that make a 15 that and add to each other to make a -15

-15

/ \

1 -15

3 -5

(X+3)(x-5)=0

x+3=0 OR x-5=0

x=-3 x=5

The Fourth and Last is the Most flipped up one because there's 2 Methods of doing it! The First Method is called Australian Method which is less steps(not really) for solving but you have to understand it! And the Second Method is called Decomposition which has equal amount of steps and is Waaaaaay easier to understand if ur the type who likes Step-by-step. Now I'm going to show you each method with the sample example and with the step next 2 them.

Australian: Step 1:Write the coefficient at the front of each

bracket& as a denominator;break the letter term up

Step2: Multiple 1st&last (which is 3m2 and -4 which makes an overall -12)

3m2 -11m-4

Stp1:(3m-12)(3m+1) Step 3: Find two #'s that multiply to -12 & add to -11

____________

3

3(m-4)(3m+1) Step4: Common Factor

___________

3

(m-4)(3m+1) Step5: Get rid of Demoniator

Decomposition:

Step0: Look for Common Factor!

Step1: Multiply 1st & Last #s (which is -12)

Step 2: Find two #'s that multiply to -12 & add to -11(which are -12,+1)

3m2 -11m-4 Step 3:Break the middle term into a sum of these two #s (which makes it be -12m+m)

3m2-12m+m-4 Step4:Take everything common

3m(m-4)+1(m-4)

(m-4)(3m+1) Step5: Factor by grouping

And TA-DA UR DONE!!!!!!!!!!!!!!!!!XD

So these were your 4 different types of Factoring! I hope u can understand my "lesson" if that's what u wanna call this. Now i gotta get back to studying for my freaking math test that's tomorrow, and as u can tell I'm doing an "all-nighter". So have a "fun" time trying to understand this(doubt there is such thing as *fun* in math), if i made u even more confused well than all i came do is say my bad get a tuitor or ask a teacher. Umm if u have anymore questions than just comment on this post.... :D

Later ppls~ xD

Yula K.

P.S this is my first post so don't except perfect especially with how my post looks I'm extremely frusterated with how it looks soo try ur best to understand this chaos...Soooooooo Sorrry