The zeros of a function f(x) are the values of x that cause f(x) to be equal to zero
One of methods to find the zeros of polynomial functions is The Factor Theorem
It is used to analyze polynomial equations. By it we can know that there is a relation between factors and zeros.
let: f(x)=(x−c)q(x)+r(x)
If c is one of the zeros of the function , then the remainder r(x) = f(c) =0
and f(x)=(x−c)q(x)+0 or f(x)=(x−c)q(x)
Notice, written in this form, x – c is a factor of f(x)
the conclusion is: if c is one of the zeros of the function of f(x),
then x−c is a factor of f(x)
And vice versa , if (x−c) is a factor of f(x), then the remainder of the Division Algorithm f(x)=(x−c)q(x)+r(x) is 0. This tells us that c is a zero for the function.
So, we can use the Factor Theorem to completely factor a polynomial of degree n into the product of n factors. Once the polynomial has been completely factored, we can easily determine the zeros of the polynomial.
