In this video I introduce three theorems that are very useful to solve problems related to polynomials. The Factor Theorem basically says that if f(x) is a polynomial and f(c)=0 then x-c is a factor of f(x) and that if x-c is a factor of f(x) then f(c)=0. The second theorem says that if f(x) is a polynomial of degree n, then it has at most n distinct real zeros. The Rational zeros theorem states that if f(x) is a polynomial with integer coefficients and p/q is a zero od f(x) then p is a factor of the constant term and q is a factor of the leading coefficient.
In this video we use these theorems to find all the rational zeros of a polynomial and to factor the polynomial.