i'm so confused on how to do this problem the way it is supposed to be done.
For what integers does divide in .
i know how to test for reduce all the coefficents to fit in and use the division algorithm to test whether it is a zero.
but how in the world do i do it for the general case?
id start with doing it with a=1,2,... until i found some sort of pattern with primes or something. but its finals time right now, and i have no time for that kind of exhaustive calculating for a homework prob. i just know there's gotta be a better way.
my pathetic attempt:
must be 0.
so, im thinking that 'plug a into x, so that once the equation is solved i can then reduce the final value to fit in '
i ran over a bunch in my head, and if what i said above is right, then factors of 12 = a
so, a = 1, 2, 3, 4, 6, and 12
(the math to my argument for a=6 -- a=x so (6)(6) + 12 = 48, but 48 must live in which is 0, voila)
?? right track ??