Question

Find the quotient. (12x 2 - 10x -12) ÷ (3x + 2)

2x - 3
4x + 6
3x + 2
4x - 6

Answer 1

`4x - 6`

Step-by-step explanation

The given quotient is

`\frac{12 {x}^(2) - 10x - 12}{3x + 2}`

We split the middle term to obtain;

`\frac{12 {x}^(2) - 18x + 8x- 12}{3x + 2}`

Factor:

`(6x( 2x - 3) + 4(2x- 3))/(3x + 2)`

`(( 2x - 3)(6x+ 4))/(3x + 2)`

`(2( 2x - 3)(3x+ 2))/(3x + 2)`

`= 2(2x - 3)`

`= 4x - 6`

The last choice is correct.