How do you factor $12r^2 - 7r - 12$ by grouping?

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Answer 1 · 2016-08-18T20:58:47

$12r^2-7r-12=(4r-3)(3r-4)$

We need to find how to split the middle term. To do that, use an AC method:

Look for a pair of factors of $AC = 12*12 = 144$ which differ by $B=7$

The pair $16, 9$ works, so we find:

$12r^2-7r-12$

$=12r^2-16r+9r-12$

$=(12r^2-16r)+(9r-12)$

$=4r(3r-4)+3(3r-4)$

$=(4r-3)(3r-4)$

How do you factor 12r^2 - 7r - 1212r^2 - 7r - 12 by grouping?