Question

explain one of the theorems that you would use to find the zero of higher degree polynomial

Answer 1

The zeros of a function f(x) are the values of x that cause f(x) to be equal to zero
There are many theorems to find the zeros of the polynomial functions and one of them is The Factor Theorem

The Factor Theorem can be used to analyze polynomial equations. By it we can know that there is a relation between factors and zeros.

let:  f(x)=(x−a)q(x)+r.

If a is one of the zeros of the function , then the remainder r =f(a) =0

 and f(x)=(x−a)q(x)+0 or f(x)=(x−a)q(x)

Notice, written in this form, x – a is a factor of f(x)

the conclusion is:  if a is one of the zeros of the function of f(x), 
then x−a is a factor of f(x)

And vice versa , if (x−a) is a factor of f(x), then the remainder of the Division Algorithm f(x)=(x−a)q(x)+r  is 0. This tells us that a is a zero.

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.