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Factoring Trinomials by Grouping

Factoring Completely General Quadratic Trinomials:

WHAT TO DO:	HOW TO DO IT:
Example: Given: 3x² − 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: 3x² − 11xy + 6y² 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:	3x² - 9xy - 2xy - 6y²
Factor common factors	3x(x - 3y) - 2y(x - 3y)
Factor common terms in ( ... )	(x - 3y)(3x - 2y) Answer
Check by multiplying FOIL: