In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial has a factor if and only if (i.e. is a root). Factor Theorem is a special case of Remainder Theorem. Remainder Theorem states that if polynomial ƒ(x) is divided by a linear binomial of the for (x - a), then the remainder will be ƒ(a). Factor Theorem states that if ƒ(a) = 0 in this case, then the binomial (x - a) is a factor of polynomial ƒ(x). The remainder theorem tells us that for any polynomial f(x) if you divide it by the binomial x-a, the remainder is equal to the value of f(a). The factor theorem tells us that if a is a zero of a polynomial f(x), then (x-a) is a factor of f(x), and vice-versa. The remainder theorem is an application of Euclidean division of polynomials. The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial (x - a) is equal to f(a).x-a is a divisor of f(x) if and only if f (a) = 0.