$f\left(x\right)$ is cubic polynomial with real coefficient and its leading coefficient = 1 and $g\left(x\right)$ is continuous function on R such that  $f\left(x\right)\cdot g\left(x\right)=(x^2+3x+2)$ and  $g(-1)=1$

	List-I		List-II
(I)	If $f\left(0\right)$ is integer, then	(P)	when$f\left(0\right)$  also takes maximum integral value is $-\frac{1}{3}$
(II)	If  $f^{\text{'}}\left(0\right)$ is integer, then	(Q)	the number of integral values of $f\left(0\right)$  is 7
(III)	The maximum value of  $g\left(x\right)$	(R)	when $f\left(0\right)$ also takes maximum integral value is  $1$
(IV)	The minimum value of   $g\left(x\right)$	(S)	when $f\left(0\right)$ also takes minimum integral value is  $-\frac{1}{8}$
		(T)	number of integral value of $f\left(0\right)$ is 3

The correct option is: