If p is prime number, which of the following statements must be true?

If p is prime number, which of the following statements must be true?

I. (p + 3)*(p + 5)*(p + 9) must be divisible by 8
II. (6p + 1)*(6p – 1) must be divisible by 6
III. (p2 – p)*(p + 1) must be divisible by 3

(A) I only
(B) III only
(C) I and II
(D) II and III
(E) I, II and III

I) (p + 3)*(p + 5)*(p + 9) => If p is even i.e. 2 then all terms will be odd and wouldn't be divisible by 8. Though if p is an odd prime number then expression would be divisible by 8 - NOT ALWAYS TRUE

II) (6p + 1)*(6p – 1)= \(36p^2-1\) when this expression is divided by 6 the first terms is divisible by 6 and thus the remainder will always be -1 => 5
NEVER TRUE

III) (p^2-p)(p+1) => (p-1)*p*(p+1) => Multiplication of 3 consecutive terms.
For p \(\geq{ 2}\) the expression above will always be divisible by 3 - MUST BE TRUE

Answer - B