Steps | Factors | ||
1. | Split the co-efficients in a manner that the ratio of the first co-efficient 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 |
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2. | Use the ratio for one of the factors. | In this case, from 1:2 we get: x + 2 |
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3. | Now divide the first co-efficient by the first co-efficient of the factor, and the independent part with the independent part of the factor. | In this case, 3/1 = 3 And, 4/2 = 2 |
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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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