Let f =
The roots of
are -3,1. (or (x+3)(x-1) are factors of this equation)
By remainder theorem (x-a) is a factor of a function f, iff f(a) = 0
We need to show that (x+3) and (x-1) are also factors of
. This can be shown by the above discussed remainder theorem.
It can be checked that f(1) = 0 and f(-3) = 0, Hence the
is a factor of