Question

Q = x^3 â xGiven that x is a positive integer such that x ⥠75, which of the following is the remainder when Q is divided by 6?

A. 0B. 1C. 3D. 5E. Cannot be determined by the information provided

Answer 1

A) 0

Explanation:

Given that

`Q=x^(3)-x\\\\x(x^(2)-1)\\\\x(x+1)(x-1)`

Divisor = 6 = 3*2

`(Q)/(D)=((x)(x+1)(x-1))/(6)\\\\(Q)/(D)=((x)(x+1)(x-1))/(2 * 3)\\`

As it can be see that x ≥ 75 and Q is product of three consecutive terms (x-1), x, (x+1) which is always completely divisible by 2, 3 and 6. So remainder is zero