What is the Remainder Theorem , How to use the Remainder Theorem , How to use the remainder and factor theorem in finding the remainders of polynomial divisions and also the factors of polynomial divisions, How to factor polynomials with remainders, with video lessons, examples and step-by-step solutions. Learn how to use the remainder theorem to find the remainder of a polynomial division by a linear polynomial. See the statement, proof, and examples of the remainder theorem and its applications in factoring polynomials. The remainder theorem states – if you divide a polynomial P (x) by x - a, the remainder would be P (a)...Let me explain. Going back to the previous example, here's the polynomial we were dividing.