Greatest Commen  Factor

Find the GCF
                                   8x2 – 2x 

1. Find the largest number that will divide into all the coefficients evenly. 
Coefficients – 8, 2
The largest number that will divide into both of them is 2.

2. Find the largest variable that will into all the coefficients evenly.
                                                        *choose the variable with the smallest exponent*
The largest variable that will go into both of them is x.

3. Put both of them together.
                       GCF = 2x

Factoring

·         Factoring is the opposite of
      expanding and simplify. It means
      to write as a product.     
                                                          Expanding 
                                                               (x + 2) (x – 2) à x2 – 4 
                                                                3 x 2 àààà 6
       Factoring
X2 – 4 à(x + 2) (x – 2)
6 ààà3 x 2 

6y3 – 24y2
The easiest way to factor is to find the GCF.
GCF : 6y2  

1.      Find the GCF .
2.      Wright down the GCF and open the Brackets.
3.      Divide the polynomial by GCF and check the brackets.
4.      Check by expanding.
                                                                           6y3 – 24y2
                                                                     1.      GCF : 6y2
                                                                     2.      6y2(
                                                                     3.      6y2(y – 4)
                                                                     4.      6y2(y – 4)
                                                                           6y3 – 24y2

Product & Sum

Find two numbers that:
Add to give you 8:    2   +    6     = 8
Multiply to give you 12: 2 x6  = 12


Factoring Trinomials

Factor 6x2 + 3x + 9                                              6x2 + 3x + 9                         
                                                                             3(2x2 + 8x +12)
GCF: 3
Factor     x2 +8x +12
                                                                1(x2 +8x +12)
    GCF: 1                                                 We cannot factor this trinomial
                                                                by simply finding the GCF.
     This is another way of factor
      x2 +8x +12 – product                    The next step is to 
      Find 2 numbers that have                place those numbers in      
      a sum = 8                                       brackets.
      a product = 12                                (x + 2)(x + 6)
      The number are                               x2 + 6x + 2x + 12
       2 & 6                                             x2 + 8x + 12