find the quotient and remainder using long division. \[ \frac{0 x^{2}-x+5}{3 x^{2}-9 x} \] quotient \( \square \) remainder \( \square \)

To perform the polynomial long division, we are dividing   Dividend: 0·x² – x + 5   (which is equivalent to –x + 5)   Divisor: 3x² – 9x Step 1. Compare the degrees:   The dividend has degree 1 (since the highest power of x is 1) and the divisor has degree 2.   Since the degree of the dividend is lower than the degree of the divisor, no term in the quotient will allow the leading term of the dividend (0·x²) to match that in the divisor. Step 2. Conclusion from degree comparison:   The quotient is 0, and what remains is the original dividend (–x + 5). Thus, using long division:   Quotient = 0   Remainder = –x + 5 This satisfies the division algorithm:   Dividend = (Divisor × Quotient) + Remainder So, the final answer is:   Quotient: 0   Remainder: –x + 5