Final answer:
The question lacks the necessary divisor to perform long division on the polynomial. We need the divisor to apply the long division method and calculate the quotient and remainder, following rules like the Division of Exponentials.
Step-by-step explanation:
The student's question is incomplete because it does not specify the divisor for the long division process. To find the quotient and remainder, one needs to divide the given polynomial — f(x)=(27x⁴-15x³+21x²-18x+18) — by a specific polynomial or monomial divisor using the long division method. Without the divisor, we cannot execute the division process. Normally, you align the dividend and divisor based on the highest degrees of the terms and repeatedly subtract multiples of the divisor until you are left with a remainder that has a lesser degree than the divisor or is zero. An important aspect to remember is that the exponents of variables are managed by subtraction when you perform the division of a term from the dividend by a term from the divisor, consistent with the Division of Exponentials rule.