What are necessary and sufficient conditions for a linear polynomial to be a factor of a given polynomial?
Suppose you are given a polynomial:
#f(x) = a_n x^n + a_(n-1) x^(n-1) +...+ a_1 x + a_0#
and a potential linear factor:
where all of
This immediately allows you to rule out many possibilities, but is not a sufficient condition.
What is sufficient is if
In fact this last condition is both necessary and sufficient regardless of whether the coefficients are integers, rational, real or even complex numbers.