The likelihood is that because we've been told to divide the quadratic by a linear expression, it may perfectly factorize and the linear expression is, in fact, one of the two factors so we can use it to find the other factor by inspection:
3x would have to multiply by 5x to get the 15x² term in the quadratic.
-3 would have to multiply by -3 to get the 9 term in the quadratic.
The second factor would, therefore, be (5x - 3) if the linear divisor is actually a factor. In this case, it is, which we can confirm by expanding.
15x² - 24x + 9 = (3x - 3)(5x - 3)
So:
(15x2 – 24x + 9) ÷ (3x – 3) = 5x - 3
