Fun with Factoring

Fun with Factoring!

Hello! My name`s Vincent. The one who sits next to Aron, the one who picked me to scribe today (This is your fault, you`re supposed to pick Shubham, you traitor. haha,just kidding!)

So in this blog, I`m going to discuss what I learned in Mr. P`s class, which is FACTORING.
There are a lot of ways to factor numbers, and one of them is finding the GCF(Greatest Common Factor)The GCF of two or more monomials is the greatest common factor that divide each of the monomials.
Example:
A. 7x² + 35x =                 7x(x + 5)

You can also FACTOR BY GROUPING, If a polynomial contains four or more items. It may be useful to group them together and factor out a common factor from each group.
Example:        
 B. 3x + 9y + 5xz + 15yz =      (3x + 9y) + (5xz + 15yz)
                              3(x + 3y) + 5z(x + 3y)
                            (3 + 5z) (x + 3y)
Another way of factoring is 
FACTORING THE DIFFERENCE OF TWO SQUARE
Sometimes an expression will be of the form (ax)² - b², which is similar to   a²b² - b². These expressions can be factored as follows: (ax)² - b² = (ax + b)(ax - b).  
Example:                
C. x² - 9 =                      (x)² - (3)²
                             (x + 3)(x - 3)

There`s also a way by FACTORING DIFFERENCE OF CUBES.Used for binomials that are a difference of two perfect cubes.
                        x³ - y ³ = (x - y)(x² + xy + y²)
Example:
D. x³ - 8 =                  (x)³  - ( 2 )³           
                       (x - 2)(x² + 2x + 4)       

You can also try FACTORING SUM OF CUBES.
Used for binomials that are a sum of two perfect cubes.
                         x ³ + y ³ = (x + y)(x² - xy + y²)
Example:
E. x³ + 27 =                  (x)³  + ( 3 )³           
                       (x + 3)(x² - 3x + 9) 

Another way of factoring is 
FACTORING PERFECT SQUARE TRINOMIALS.The trinomilas x² + 2xy + y² and   x² - 2xy + y² are called perfect square trinomials:
                    x² + 2xy + y² = (x + y)²
                    x² - 2xy + y² = (x - y)²
Example: 
F. 16x² + 24 + 9 =         (4x)² + 2 . 4x . 3 + (3)²                                              (4x + 3)²

Then there`s the FACTORING TRINOMIALS OF THE FORM x² + bx + c WITH LEADING COEFFICIENT 1
When given an expression of this form, we can break it into two binomials that can be multiplied together to get the given expression. 
x² + bx + c = (x + u)(x + v), where u and v are integers that satisfy the following:

1. uv = c
2. u + v = b

Here are some tips for this kind of factoring.
1. If c is (+) = u and v have the same sign.
    If b is (+) = u and v are (+)
    If b is (-) = u and v are (-)
2. If c is (-) = u and v have opposite signs.

Example: 
G. x²+ 7x + 12 =        a = 1, b = 7, c = 12
                            C > 0, B > 0
                              u.v = 12
                              u + v = 7 
                               3 , 4
                        (x + 4)(x + 3)




You can also use trial and error method which is a bit time consuming when your doing an exam.

Well, those are the factoring ways Mr. P taught us in class and I hope all the readers of this blog will like it.



Oh yeah since we haven't got donuts yet, here's something to motivate you :)