Simple equation - prove division

Question

this should be simple. I am helping my son with one assignment but I simply cannot solve it. I really exhausted ideas. The problem is: prove that $\displaystyle {(m^2 + 5m)(m^2 + 5m + 10) + 24}$ can be divided by 24. Any hint?

Answer 1

$A = (m^2+5m + 5)^2 - 1 = (m^2 + 5m + 6)(m^2 + 5m + 4) = (m+1)(m+2)(m+3)(m+4)$ divisible by $4! = 24$.