PolynomialsAlgebra Level 5
Johanz says to Sandra, "I am thinking of a polynomial whose roots are all positive integers. The polynomial has the form \(P(x)=2x^3-2ax^2+(a^2-81)x-c\) for some positive integers \(a\) and \(c\). Can you tell me the values of \(a\) and \(c\)?"
After some calculations, Sandra says, "There is more than one such polynomial."
Johanz says, "You’re right. Here is the value of \(a\)." He writes down a positive integer and asks, "Can you tell me the value of \(c\)?"
Sandra says, "There are still two possible values of \(c\)."
Find the sum of the two possible values of \(c\).