Question

Completely factor 12x² - 7x - 12.




A.
(4x + 3)(3x - 4)



B.
(12x + 1)(x - 12)



C.
(12x - 12)(x + 1)



D.
(4x - 4)(3x + 3)

Answer 1

You can solve this a few ways. You could use the quadratic formula but I am going to use the grouping method.

$12x^2 - 7x - 12$
First find two numbers that equal -12 when you multiply them but also equals -7 when you add them. Two numbers that do just that are -16 and 9

Now use the two numbers and put it in group form
$12x^2 - 7x - 12$
$12x^2 - 16x + 9x - 12$
$(12x^2 - 16x) + (9x - 12)$

Now factor out the groups
$(12x^2 - 16x) + (9x - 12)$
$4x(3x - 4) + 3(3x - 4)$
$(4x + 3)(3x - 4)$
The answer is A