
Steps  Factors  
1.  Split the coefficients in a manner that the ratio of the first coefficient to one of them is the same as the other to the independent term.  In this case, 8 = 6 + 2 gives: 3:6 = 2:4 is in ratio 1:2 

2.  Use the ratio for one of the factors.  In this case, from 1:2 we get: x + 2 

3.  Now divide the first coefficient by the first coefficient of the factor, and the independent part with the independent part of the factor.  In this case, 3/1 = 3 And, 4/2 = 2 

4.  Use this to form the second factor.  In this case, 3 and 2 gives: 3x + 2 Therefore, the factors are: (x + 2) (3x + 2), which is the answer! 
Clearly, 12 = 2 + 10 gives: 4:2 = 10:5 is in ratio 2:1 So, 2x + 1 is one factor Again 4/2 = 2 and 5/1 = 5 So, the other factor is: 2x + 5 Thus, the factors are: (2x + 1)(2x + 5) 
Clearly, 14 = 20 + 6 gives: 15:20 = 6:8 is in ratio 3:4 So, 3x  4y is one factor Again 15/3 = 5 and 8/4 = 2 So, the other factor is: 5x + 2y Thus, the factors are: (3x  4y)(5x + 2y) 
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