Consider the function ​g(x)=x4+2x3+px2+qx−4, where ​p,q∈R​ are constants. When ​g(x)​ is divided by ​(x−1), the remainder is ​−12, and when divided by ​(x+3)​ the remainder is ​20. Find the values of ​p​ and ​q.

Consider the function ​g(x)=x4+2x3+px2+qx−4, where ​p,q∈R​ are constants. When ​g(x)​ is divided by ​(x−1), the remainder is ​−12, and when divided by ​(x+3)​ the remainder is ​20. Find the values of ​p​ and ​q.