The quotient of the expression is
. Hence, option (a) is correct.
Step 1: Set up the long division.

Step 2: Divide the first term of the dividend by the first term of the divisor.
The leading term of the dividend is
, and the leading term of the divisor is
. Dividing
by
, gives 3x
Step 3: Multiply the divisor by the quotient.

Step 4: Subtract the product from the dividend.
Subtracting
from
gives
.
Step 5: Bring down the next term of the dividend.
The next term of the dividend is -z-4.
Step 6: Repeat steps 2-5 until the remainder is either zero or a polynomial of lower degree than the divisor.
Dividing
by
gives
. Since the remainder is 15-z-4, which is a polynomial of lower degree than the divisor, the division is complete.
Step 7: Write the quotient and remainder.
The quotient is
, and the remainder is 15-z-4. Therefore, the final answer is
