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?

Answer 1

Answer:

A) 0

Step-by-step explanation:

Given that

$Q=x^{3}-x\\\\x(x^{2}-1)\\\\x(x+1)(x-1)$

Divisor = 6 = 3*2

$\frac{Q}{D}=\frac{(x)(x+1)(x-1)}{6}\\\\\frac{Q}{D}=\frac{(x)(x+1)(x-1)}{2 \times 3}$

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