Well, the linear term is easy: if we take 1 from each root then the sum of those roots will be decreased by 2:

S' = S - 2

S' = 4 - 2 = 2

The product is a bit tougher and I don't know how to get this result without essentially solving the problem. What I did was this:

The original expression is

(x - a)(x - b)

So we want

(x - (a - 1))(x - (b - 1)) = x^2 - (a + b - 2)x + (ab - (a + b) + 1)

So the last term will be:

P' = P - S + 1

P' = -6 - 4 + 1 = -9

But I really don't know how to prove this result without working it out as above (which seems to be cheating to me.)

-Dan