Polynomial Theorems: Remainder, Factor, Division [IB Math AA HL]

The speaker introduces the factor and remainder theorems for polynomials, explaining that the remainder theorem allows one to find the remainder of a polynomial division by substituting a value 'k' into the polynomial, where the divisor is (x - k). The factor theorem is presented as a special case where if the remainder (P(k)) is zero, then (x - k) is a factor of the polynomial. The video then demonstrates these concepts through two examples: finding the remainder of a polynomial divided by (x + 2), and finding a constant 'k' in a polynomial given a factor, then fully factorizing the cubic function using polynomial long division. The speaker emphasizes the importance of understanding these theorems and the factorization process for IB Math exams.