Factoring

Hey, what's up guys, it's Chris Tabios and I am going to explain the different methods on how to factor polynomials which we covered a awhile ago. 

The first method that we learned was finding the GCF (Greatest Common Factor). To summarize, the Greatest Common Factor is the greatest term that can be divided into each of the terms of the the given polynomial. 

                     Ex. 5x²+35x

 The GCF would be 5x because 5x goes into 5 and 35 without having to deal with any difficult numbers. Once you come up with the GCF all you have to do is divide each term of the polynomial by it. 

For this example, the final answer would be 5x(x+7).

The second factoring method we covered is Factoring By Grouping. Sometimes with polynomials with four or more terms, the easiest way to completely factor the polynomial is by grouping up the terms.In order to do this you would have to split-up the polynomial into groups.

Ex. 5x+5y+zx+zy 

(5x+5y)      (zx+zy) 

*Remember to keep the (+) and (-) signs as they are *

After you group up the terms, you will have to once again have to find the GCF of the terms. Following the final answer format of the GCF example, you would get:

5(x+y) and  z(x+y)

The final step is to write it out as 

(x+y)(5+z) 

The next factoring method we learned is Factoring the Difference of Two Squares. To do this, all you have to do is remember (ax)²-b²= (ax+ b)(ax-b)

Ex.  x²-9 =
 (x+3)(x-3) 

Another method of factoring polynomials is Factoring the Difference of Cubes. to put it simply, it is used for binomials that are a difference of two perfect cubes.  The form to remember is  x³-y³=(x-y)(x²+xy+y²)


Ex. x³-27
 x³-3³=(x-3)(x²+3x+9)
*Turn terms into x³*

There is also a method called Factoring the Sum of Cubes, which is the same concept, except the form is x³+y³=(x+y)(x²-xy+y²)

The final two methods of factoring polynomials are Factoring Perfect Square Trinomials and Factoring Trinomials with a leading coefficient of other than 1

Factoring Perfect Square Trinomials:

 x² + 2xy + y² and x² - 2xy + y² are called perfect square trinomials
 This is the form that will be used:

x² + 2xy + y² = (x + y)² and x² - 2xy + y² = (x - y)²

 16x² + 24 + 9 = (4x)² + (2)(4x )( 3 )+ (3)²=
(4x + 3)²


Factoring Trinomials With a Leading Coefficient Other Than 1:

 To factor these trinomials you must first multiply the the first and last numbers, then you would have to find two numbers that would add up to the middle term and multiply together to turn into the new number.



Ex. 5x² +13x-6 

(5) x (-6) = -30 

5x² +15x-2x-6

5x(x+3) -2(x+3)

(5x-2)(x+3)