# Polynomials

Algebra 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 $$c$$.

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