The remainder theorem is a fundamental concept in algebra that is used to find the remainder when a polynomial is divided by a linear expression. The theorem states that when a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a) . This means that if we divide a polynomial by a factor (x - a), the remainder will be the same as the value of the polynomial when we substitute x with a. The remainder theorem can be used to find the remainder when a polynomial is divided by another linear polynomial, to help in the factorization of polynomials, and to determine the zeros of a polynomial. However, the theorem only works when the divisor is linear. The remainder theorem can be proved by Euclids Division Lemma.