Package of problems

1. Can you find a polynomial (not necessarily a quadratic) with integer coefficients which has $\sqrt{2}+\sqrt{3}$ as a root? What other roots (if any) does it have?
2. Can you find a polynomial with integer coefficients which has $1+\sqrt[3]{2}=1+2^{\frac{1}{3}}$ as a root? What other roots (if any) does it have?
3. Can you find a polynomial with integer coefficients which has $\sqrt[3]{2}+\sqrt[3]{4}=2^{\frac{1}{3}}+2^{\frac{2}{3}}$ as a root? What other roots (if any) does it have?