find the largest n such that n+10 divides n^3 + 100..

Here n³ + 100 = n³ + 1000 - 900

                     = (n + 10)(n² + 100 + 10n) - 900

here (n + 10)(n² + 100 + 10n) is divisible by n + 10 so now question reduces to 900 should be divisible by n+10

Let us say 900 = (n + 10) x (some natural no.)

 for largest value of n natural no. is 1.

 Hence 900 = n + 10

so n = 890

This is your ans.