ANSWER
[tex]4x - 6[/tex]
EXPLANATION
The given quotient is
[tex] \frac{12 {x}^{2} - 10x - 12}{3x + 2} [/tex]
We split the middle term to obtain;
[tex]\frac{12 {x}^{2} - 18x + 8x- 12}{3x + 2} [/tex]
Factor:
[tex]\frac{6x( 2x - 3) + 4(2x- 3)}{3x + 2} [/tex]
[tex]\frac{( 2x - 3)(6x+ 4)}{3x + 2} [/tex]
[tex]\frac{2( 2x - 3)(3x+ 2)}{3x + 2} [/tex]
[tex] = 2(2x - 3)[/tex]
[tex] = 4x - 6[/tex]
The last choice is correct.
