Understanding the remainder theorem

The document discusses using the remainder theorem to find the remainder of a polynomial function divided by a binomial function without fully performing the division. It provides two examples: 1) When f(x) = x^3 - 3x^2 + 7 is divided by g(x) = x + 2, the remainder is -13. 2) When f(x) = x^3 - 3x^2 + 5x - 1 is divided by g(x) = x - 1, the remainder is 2. The key steps are to set the binomial factor equal to 0 to find the value to substitute into the polynomial, then evaluate the polynomial at that value to determine the remainder.