2014/056) p(x) = x^3 -6x^2+ 17x, p(m) = 16, p(n) = 20 find m+ n

we have P(x) = x^3 - 6x^2 + 17x
so we have P(x+2) = x^3 + 5x + 18 ( I take x+2 to eliminate the $x^2$ term to see in case we get odd function)

now
P(m) = (m-2)^3 + 5(m-2) + 18 = 16

or (m-2)^3 +5 (m-2) = - 2...(1)

P(n) = (n-2)^3 + 5(n-2) + 18 = 20

or (n-2)^3 + 5(n-2) = 2 ....   (2)

from (1) and (2) as

f(x) = x^3 + 5x

f(m-2) + f(n-2) = 0

so  m- 2 + n -2 = 0

or m+n = 4