polynomial division!!!!plz help

[ashishunleashed]

The remainder when n ^12- 12 ^n2 + 132 is divided by 11 is

pl help with this que and other such que, where we are asked to find remainder of a high power polynomial

[jnelson0612]

The remainder when n ^12- 12 ^n2 + 132 is divided by 11 is

pl help with this que and other such que, where we are asked to find remainder of a high power polynomial

To me the easiest way to solve this is to plug in some easy numbers. Clearly the remainder is the same for all values of n, so why not check out a few?

If I choose n is 0, I get 0^12 - 12^(0)^2 + 132 = 132. 132 is divisible by 11, so no remainder.

If I choose n is 1 and run it through the formula above, I get 1 - 12 + 132 = 121. 121 is divisible by 11, so no remainder.

At this point I would feel very comfortable answering that zero is the remainder, but if you want you could even plug in 2. You would get 4096 - 48 + 132 = 4180, which is also divisible by 11 (38 times). Clearly zero is the answer.