Problem Solving (PS) | Re: If k is a positive integer, what is the remainder when (k + 2)(k^3 – k

If k is a positive integer, what is the remainder when (k + 2)(k^3 – k) is divided by 6 ?

(k+2)(k^3–k)
=(k+2)k(k^2–1)
=(k+2)k(k–1)(k+1)
=(k−1)k(k+1)(k+2)

now, we know, the product of 3 consecutive numbers is always divisible by 6.
so, (k+2)(k^3–k) is divisible by 6.

the remainder when (k + 2)(k^3 – k) is divided by 6 = 0

correct answer A

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