If n is a positive integer, is n^3 + 4n^2 - 5n divisible by 8 ?
(1) n = 4b + 1, where b is a positive integer.
(2) n^2 – n is divisible by 24.
The only things to point out or add if you will are the following
Question stem = Factorizing one gets (n)(n+5)(n-1)
n = 4b+1
Now (4b) and (4b+1) are consecutive integers
Therefore one of them must be odd and one even, obviously 4b is the even one
So 4b is a multiple of 4 and 4b +6 is even so we have a multiple of 8
n(n-1) divisible by 24 means that either n or n-1 is divisible by 3 and that one of them, the even one, will be divisible by 8
Since we have both terms in our initial factorization then YES it is a multiple of 8
Is this clear?
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