Final answer:
The remainder theorem finds the remainder of a polynomial divided by a linear factor by evaluating the polynomial at the root of the divisor. A specific example isn't provided, but the theorem is explained, and its use in terms of calculators and exponential division is noted.
Step-by-step explanation:
The question seems to be incomplete because it references the remainder theorem but does not provide a specific polynomial or a value to evaluate it at. However, I can explain how to use the remainder theorem. The remainder theorem states that if a polynomial f(x) is divided by a linear divisor x - a, the remainder of that division is f(a). So, to find the remainder using the remainder theorem, simply evaluate the polynomial at the value that makes the divisor zero. For example, if you have a polynomial f(x) to be divided by x - 2, find f(2) to determine the remainder.
To compile a clearer example, let's consider a polynomial f(x) = x^2 - 3x + 2 and we want to find the remainder when it's divided by x - 1. According to the remainder theorem, we would evaluate the polynomial at 1: f(1) = 1^2 - 3(1) + 2, which simplifies to f(1) = 0. Therefore, the remainder is 0 when f(x) is divided by x - 1.
In application, this could be used with TI-83, TI-83+, TI-84, or TI-84+ calculators for computation. Additionally, an understanding of exponential division is sometimes needed when dealing with polynomials containing exponential terms.