let $g$ be a natural number how to show that $30$ divides $(-8 g^5+20 g^4-50 g^3+115 g^2-167 g+90)$?
my guess: $30$ divides $90$ so it is enough to show that $30|-8 g^5+20 g^4-50 g^3+115 g^2-167 g = g(-8 g^4+20 g^3-50 g^2+115 g-167) $ now if $30|g$ we are done, otherwise we have to show that $30|-8 g^4+20 g^3-50 g^2+115 g-167$ , I don't know how to go further..