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Assuming you mean 12x2 - 5x - 2, use the reverse FOIL method. But, first, multiply the two end number together (12 * -2 = -24). Then find two numbers whose product is -24 and sum is -5. These two numbers are 3 and -8.
3 * ( -8 ) = -24 and 3x + ( -8x ) = -5x
Next, we use those factors found in the previous step and group them together.
12x2 - 5x - 2
12x2 + 3x - 8x -2
( 12x2 + 3x ) ( -8x - 2 )
Next, take out the common factors from each group
( 12x2 + 3x ) ( -8x - 2 )
3x ( 4x + 1 ) - 2 ( 4x + 1 )
Lastly, group the two ungrouped terms multiplied by their common factor ( 4x + 1 )
3x ( 4x + 1 ) - 2 ( 4x + 1 )
( 3x - 2 ) ( 4x + 1 )
Next, we check the work by usingthe FOIL method.
( 3x - 2 ) ( 4x + 1 )
F ... 3x * 4x = 12x2
O ... 3x * 1 = 3x
I ... -2 * 4x = -8x
L ... -2 * 1 = -2
12x2 + 3x - 8x - 2
Combine like terms
12x2 - 5x - 2
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