Question

what is a factor in respect to polynomial functions

Answer 1

A factor usually a monomial or binomial that cannot be factored further that when set equal to zero and solved will provide one or more roots/zeros/x-intercepts of the original polynomial function.

For example the factors of \f(x)=[x ^{2}-3x-4\]
are \[(x-4)(x+1)\]

Now set each factor equal to zero and you get x=-1 or x-4 when you solve.