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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Factoring Trinomials by Grouping

## Factoring Completely General Quadratic Trinomials:

 WHAT TO DO: HOW TO DO IT: Example: Given: 3x 2 − 7x − 6 GN 3Â·6 = 18 The last sign is â€œ−â€ so find the pair of factors of 18 that has a difference of  7. The largest factor of the pair gets middle sign, â€œ−â€ − 9 and + 2 3x2 - 9x + 2x - 6 Group 2 Ã— 2: 3x2 − 9x + 2x −- 6 Factor common factors 3x(x − 3) + 2(x − 3) Factor common terms in ( ... ) (x − 3)(3x + 2) Answer Check by multiplying FOIL: Example: 3x 2 − 11xy + 6y 2 Look at numbers only GN: 3Â·6 = 18 The last sign is â€œ+â€ so find the pair of factors of 18 that has a sum of 11. Both of the factors of the pair get middle sign, â€œ−â€ -9 and -2 Arrange terms and group 2 Ã— 2: 3x 2 - 9xy - 2xy - 6y 2 Factor common factors 3x(x - 3y) - 2y(x - 3y) Factor common terms in ( ... ) (x - 3y)(3x - 2y) Answer Check by multiplying FOIL: