1. **State the problem:** We need to divide the polynomial $$f(x) = -33x^3 - 9x + 2$$ by the polynomial $$p(x) = x - 3$$ and find the quotient and remainder. 2. **Formula and rules:** Polynomial division is similar to long division with numbers. We divide the highest degree term of the dividend by the highest degree term of the divisor, multiply the divisor by that result, subtract, and repeat until the degree of the remainder is less than the divisor. 3. **Step 1:** Divide the leading term of $$f(x)$$ by the leading term of $$p(x)$$: $$\frac{-33x^3}{x} = -33x^2$$ 4. **Step 2:** Multiply $$p(x)$$ by $$-33x^2$$: $$-33x^2(x - 3) = -33x^3 + 99x^2$$ 5. **Step 3:** Subtract this from $$f(x)$$: $$(-33x^3 - 9x + 2) - (-33x^3 + 99x^2) = 0x^3 - 99x^2 - 9x + 2 = -99x^2 - 9x + 2$$ 6. **Step 4:** Divide the leading term of the new polynomial by the leading term of $$p(x)$$: $$\frac{-99x^2}{x} = -99x$$ 7. **Step 5:** Multiply $$p(x)$$ by $$-99x$$: $$-99x(x - 3) = -99x^2 + 297x$$ 8. **Step 6:** Subtract: $$(-99x^2 - 9x + 2) - (-99x^2 + 297x) = 0x^2 - 306x + 2 = -306x + 2$$ 9. **Step 7:** Divide the leading term by the leading term of $$p(x)$$: $$\frac{-306x}{x} = -306$$ 10. **Step 8:** Multiply $$p(x)$$ by $$-306$$: $$-306(x - 3) = -306x + 918$$ 11. **Step 9:** Subtract: $$(-306x + 2) - (-306x + 918) = 0x - 916 = -916$$ 12. **Step 10:** Since the remainder $$-916$$ is a constant (degree 0) and the divisor has degree 1, we stop here. **Final answer:** Quotient: $$-33x^2 - 99x - 306$$ Remainder: $$-916$$