Question

The largest possible number by which the expression n³-n is divisible for all the possible integral values of n is
(1) 2
(2) 3
(3) 4
(4) 6​

Answer 1

Answer:

(1) 2

Step-by-step explanation:

n³-n

n(n²-1) this expression will always give Even Value any n

n

And all even no.s are divisible by Only 2

Answer 2

n³-n = n(n²-1) = n(n-1)(n+1)

n³ - n = (n-1) (n) (n+1)

One of the values among them will be even number. so it will be divisible by 2.

Also, as there are three consecutive numbers, one of the values will be odd this means it will be divisible by 3 as well.

Since, n³-n is divisible by 2 and 3 both , therefore, n³-n is divisible by 6. (product of 2 and 3)

Among all the options 6 is largest

Hence, (4) option is correct i.e. 6.

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