Continuous mapping theorem

Suppose $X_n\to X$ almost surely, and let

$$Y_n=X_n^{3}+2X_n^{2}+3X_n+2,\qquad Y=X^{3}+2X^{2}+3X+2 .$$

Consider: (I) $Y_n\to Y$ almost surely; (II) $Y_n\to Y$ in probability; (III) $Y_n\to Y$ in law.