Question 254242
WHat we have is
{{{(3x^2 + kx + 4) / (x-2)}}} =3x-2 then k= ?
It appears you have don the division or have been told the answer.
If we divide synthetically, then we get
2 / . . 3 . . . . k . . . . .4
 . . . .  . . . . .6 . . . . .2k + 12
 . . . . 3 . . . . k+6 . . . .0
This means that 2k + 16 = 0 or k = -8.
If k = -8, then k + 6 = -2 and the quotient is
3x - 2.
Now we have a restriction on the domain; x - 2 not = 0 which means x not = 2.
Hope this makes sense.