How do you factor by grouping $12x^2-7x-5$ ?

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Answer 1 · 2015-06-06T13:00:15

The trick is to find how to split the middle $-7x$ term.

The split comes from a pair of factors of $AC=12*5=60$ whose difference is $B=7$ . The pair $12, 5$ works.

$12x^2-7x-5$

$= 12x^2-12x+5x-5$

$= (12x^2-12x)+(5x-5)$

$=12x(x-1)+5(x-1)$

$=(12x+5)(x-1)$

Answer 2 · 2015-06-06T22:02:01

When a + b + c = 0, you are advised to use the Shortcut.
One factor is (x - 1) and the other is (-c/a = 5/12).

y = (x - 1)( 12x + 5)

How do you factor by grouping 12x^2-7x-512x^2-7x-5?