Question

what is the largest integer n such that n^3+100 is divisible by n+10?

Answer 1

You get a remainder of 900 if you divide n^3+100 by n+10.

Answer 2

i don't think n+10 is going to divide n^3+100 without leaving a remainder whatever large the value of n may be

It always leaves a remainder of -900.

Answer 3

Well, the remainder is -900/(n+10)

Answer 4

You have to find the largest integer \(n\) such that \[ \frac{n^3+100}{n+10} \] is an integer.

Using long division or Ruffini's rule, we can show that:

\[ \frac{(n^3+100)}{(n+10)} = (n^2 - 10n + 100) -\frac {900}{(n + 10)}\]

so, our problem reduces to finding the largest value of n such that \(900 | (n+10) \), i.e \(\boxed{890}\)

Answer 5

Asi es...

Answer 6

@estudier: (+1) for updating me on "Asi es"!