1. **Problem statement:** Form a polynomial with zeros 6 (multiplicity 1) and 3 (multiplicity 2), and degree 3. 2. **Recall:** A polynomial with zeros $r$ of multiplicity $m$ includes the factor $(x-r)^m$. 3. **Write factors:** For zero 6 (multiplicity 1), factor is $(x-6)$. For zero 3 (multiplicity 2), factor is $(x-3)^2$. 4. **Form polynomial:** Multiply factors: $$f(x) = (x-6)(x-3)^2$$ 5. **Expand:** First expand $(x-3)^2 = (x-3)(x-3) = x^2 - 6x + 9$ 6. Multiply: $$f(x) = (x-6)(x^2 - 6x + 9)$$ 7. Distribute: $$f(x) = x(x^2 - 6x + 9) - 6(x^2 - 6x + 9)$$ $$= x^3 - 6x^2 + 9x - 6x^2 + 36x - 54$$ 8. Combine like terms: $$f(x) = x^3 - 12x^2 + 45x - 54$$ 9. **Final polynomial:** $$\boxed{f(x) = x^3 - 12x^2 + 45x - 54}$$ This polynomial has degree 3, zeros 6 (multiplicity 1) and 3 (multiplicity 2), leading coefficient 1, and integer coefficients.