1. The problem states: If a polynomial $f(x)$ is divided by $(x - a)$, then the remainder of the division is equal to $f(a)$. 2. This is a statement of the Remainder Theorem, which says that when a polynomial $f(x)$ is divided by a linear divisor of the form $(x - a)$, the remainder is the value of the polynomial evaluated at $x = a$. 3. The formula used is: $$\text{Remainder} = f(a)$$ 4. Explanation: When dividing $f(x)$ by $(x - a)$, the division algorithm states: $$f(x) = (x - a) \cdot q(x) + r$$ where $q(x)$ is the quotient polynomial and $r$ is the remainder, which must be a constant (degree less than 1). 5. To find $r$, substitute $x = a$: $$f(a) = (a - a) \cdot q(a) + r = 0 + r = r$$ 6. Therefore, the remainder $r$ equals $f(a)$. This theorem is very useful for quickly finding remainders without performing full polynomial division.